thermalfist::IdealGasFunctions Namespace Reference

Contains implementation of the thermodynamic functions corresponding to an ideal gas of particles in the grand-canonical ensemble. More...

Classes
struct	IdealGasFunctionsExtraConfig
struct	MagneticFieldConfiguration
	Magnetic field configuration. More...

Enumerations
enum	Quantity {   ParticleDensity , EnergyDensity , EntropyDensity , Pressure ,   chi2 , chi3 , chi4 , ScalarDensity ,   chi2difull , chi3difull , chi4difull , dndT ,   d2ndT2 , dedT , dedmu , dchi2dT }
	Identifies the thermodynamic function. More...
enum	QStatsCalculationType { ClusterExpansion , Quadratures }
	Identifies whether quantum statistics are to be computed using the cluster expansion or numerical integration using 32-point Gauss-Legendre quadratures. More...

Functions
double	BoltzmannDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the particle number density of a Maxwell-Boltzmann gas.
double	BoltzmannPressure (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the pressure of a Maxwell-Boltzmann gas.
double	BoltzmannEnergyDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the energy density of a Maxwell-Boltzmann gas.
double	BoltzmannEntropyDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the entropy density of a Maxwell-Boltzmann gas.
double	BoltzmannScalarDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the scalar density of a Maxwell-Boltzmann gas.
double	BoltzmannTdndmu (int N, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the chemical potential derivative of density for a Maxwell-Boltzmann gas.
double	BoltzmannChiN (int N, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionless susceptibility for a Maxwell-Boltzmann gas.
double	BoltzmannChiNDimensionfull (int N, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionfull susceptibility for a Maxwell-Boltzmann gas.
double	BoltzmannMagnetization (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the thermal part of the magnetization of a Maxwell-Boltzmann gas, m_B = dP/dB.
double	QuantumClusterExpansionDensity (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the particle number density of a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionPressure (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the pressure of a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionEnergyDensity (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the energy density of a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionEntropyDensity (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the entropy density of a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionScalarDensity (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the scalar density of a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionTdndmu (int N, int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the chemical potential derivative of density for a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionChiN (int N, int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionless susceptibility for a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionChiNDimensionfull (int N, int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionfull susceptibility for a quantum ideal gas using cluster expansion.
double	QuantumClusterExpansionMagnetization (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the thermal part of the magnetization of a Maxwell-Boltzmann gas, m_B = dP/dB.
double	QuantumNumericalIntegrationDensity (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the particle number density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationPressure (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the pressure of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationEnergyDensity (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the energy density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationEntropyDensity (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the entropy density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationScalarDensity (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the scalar density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationMagnetization (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the magnetization of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationT1dn1dmu1 (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	QuantumNumericalIntegrationT2dn2dmu2 (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	QuantumNumericalIntegrationT3dn3dmu3 (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	QuantumNumericalIntegrationTdndmu (int N, int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	QuantumNumericalIntegrationChiN (int N, int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionless susceptibility for a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	QuantumNumericalIntegrationChiNDimensionfull (int N, int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionfull susceptibility for a quantum ideal gas using 32-point Gauss-Laguerre quadratures.
double	psi (double x)
	Auxiliary function.
double	psi2 (double x)
	Auxiliary function.
double	FermiNumericalIntegrationLargeMuDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the particle number density of a Fermi-Dirac ideal gas at mu > m.
double	FermiNumericalIntegrationLargeMuPressure (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the pressure of a Fermi-Dirac ideal gas at mu > m.
double	FermiNumericalIntegrationLargeMuEnergyDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the energy density of a Fermi-Dirac ideal gas at mu > m.
double	FermiNumericalIntegrationLargeMuEntropyDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the entropy density of a Fermi-Dirac ideal gas at mu > m.
double	FermiNumericalIntegrationLargeMuScalarDensity (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the scalar density of a Fermi-Dirac ideal gas at mu > m.
double	FermiNumericalIntegrationLargeMuMagnetization (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiNumericalIntegrationLargeMuT1dn1dmu1 (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiNumericalIntegrationLargeMuT2dn2dmu2 (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiNumericalIntegrationLargeMuT3dn3dmu3 (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiNumericalIntegrationLargeMuTdndmu (int N, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiNumericalIntegrationLargeMuChiN (int N, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionless susceptibility for a Fermi-Dirac ideal gas at mu > m.
double	FermiNumericalIntegrationLargeMuChiNDimensionfull (int N, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order dimensionfull susceptibility for a Fermi-Dirac ideal gas at mu > m.
double	FermiZeroTDensity (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the particle number density of a Fermi-Dirac ideal gas at zero temperature.
double	FermiZeroTPressure (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the pressure of a Fermi-Dirac ideal gas at zero temperature.
double	FermiZeroTEnergyDensity (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the energy density of a Fermi-Dirac ideal gas at zero temperature.
double	FermiZeroTEntropyDensity (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the entropy density of a Fermi-Dirac ideal gas at zero temperature.
double	FermiZeroTScalarDensity (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the scalar density of a Fermi-Dirac ideal gas at zero temperature.
double	FermiZeroTMagnetization (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiZeroTdn1dmu1 (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiZeroTdn2dmu2 (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiZeroTdn3dmu3 (double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiZeroTdndmu (int N, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
double	FermiZeroTChiN (int N, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order susceptibility for a Fermi-Dirac ideal gas at zero temperature.
double	FermiZeroTChiNDimensionfull (int N, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the n-th order susceptibility scaled by T^n for a Fermi-Dirac ideal gas at zero temperature.
double	IdealGasQuantity (Quantity quantity, QStatsCalculationType calctype, int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Calculation of a generic ideal gas function.
double	BoltzmanndndT (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Temperature derivatives.
double	Boltzmannd2ndT2 (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the 2nd derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	BoltzmanndedT (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	Boltzmanndedmu (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.
double	Boltzmanndchi2dT (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumClusterExpansiondndT (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumClusterExpansiond2ndT2 (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the 2nd derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumClusterExpansiondedT (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumClusterExpansiondedmu (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.
double	QuantumClusterExpansiondchi2dT (int statistics, double T, double mu, double m, double deg, int order=1, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumNumericalIntegrationdndT (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumNumericalIntegrationd2ndT2 (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the 2nd derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumNumericalIntegrationdedT (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	QuantumNumericalIntegrationdedmu (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.
double	QuantumNumericalIntegrationdchi2dT (int statistics, double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.
double	FermiNumericalIntegrationLargeMudndT (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	FermiNumericalIntegrationLargeMud2ndT2 (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the second derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	FermiNumericalIntegrationLargeMudedT (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.
double	FermiNumericalIntegrationLargeMudedmu (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.
double	FermiNumericalIntegrationLargeMudchi2dT (double T, double mu, double m, double deg, const IdealGasFunctionsExtraConfig &extraConfig=IdealGasFunctionsExtraConfig())
	Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.
std::vector< double >	GetSpins (double degSpin)
	Calculate all the spin values -S, S+1,...,S-1,S.

Variables
bool	calculationHadBECIssue = false
	Whether \mu > m Bose-Einstein condensation issue was encountered for a Bose gas.
const double *	legx32 = NumericalIntegration::coefficients_xleg32_zeroone
const double *	legw32 = NumericalIntegration::coefficients_wleg32_zeroone
const double *	lagx32 = NumericalIntegration::coefficients_xlag32
const double *	lagw32 = NumericalIntegration::coefficients_wlag32

Detailed Description

Contains implementation of the thermodynamic functions corresponding to an ideal gas of particles in the grand-canonical ensemble.

Enumeration Type Documentation

QStatsCalculationType

enum thermalfist::IdealGasFunctions::QStatsCalculationType

Identifies whether quantum statistics are to be computed using the cluster expansion or numerical integration using 32-point Gauss-Legendre quadratures.

Enumerator
ClusterExpansion
Quadratures

Definition at line 41 of file IdealGasFunctions.h.

Quantity

enum thermalfist::IdealGasFunctions::Quantity

Identifies the thermodynamic function.

Enumerator
ParticleDensity
EnergyDensity
EntropyDensity
Pressure
chi2
chi3
chi4
ScalarDensity
chi2difull
chi3difull
chi4difull
dndT
d2ndT2
dedT
dedmu
dchi2dT

Definition at line 31 of file IdealGasFunctions.h.

Function Documentation

BoltzmannChiN()

double thermalfist::IdealGasFunctions::BoltzmannChiN	(	int	N,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionless susceptibility for a Maxwell-Boltzmann gas.

Computes \( \chi_n \equiv \frac{\partial^n p/T^4}{\partial (mu/T)^n} \) for a Maxwell-Boltzmann gas.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 143 of file IdealGasFunctions.cpp.

BoltzmannChiNDimensionfull()

double thermalfist::IdealGasFunctions::BoltzmannChiNDimensionfull	(	int	N,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionfull susceptibility for a Maxwell-Boltzmann gas.

Computes \( \chi_n \equiv \frac{\partial^n p}{\partial mu^n} \) for a Maxwell-Boltzmann gas.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 149 of file IdealGasFunctions.cpp.

Boltzmannd2ndT2()

double thermalfist::IdealGasFunctions::Boltzmannd2ndT2	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the 2nd derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-2].

Definition at line 1572 of file IdealGasFunctions.cpp.

Boltzmanndchi2dT()

double thermalfist::IdealGasFunctions::Boltzmanndchi2dT	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dchi2dT [fm-3].

Definition at line 1605 of file IdealGasFunctions.cpp.

Boltzmanndedmu()

double thermalfist::IdealGasFunctions::Boltzmanndedmu	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedmu [fm-3].

Definition at line 1601 of file IdealGasFunctions.cpp.

BoltzmanndedT()

double thermalfist::IdealGasFunctions::BoltzmanndedT	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedT [fm-3].

Definition at line 1586 of file IdealGasFunctions.cpp.

BoltzmannDensity()

double thermalfist::IdealGasFunctions::BoltzmannDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the particle number density of a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Particle number density [fm-3].

Definition at line 41 of file IdealGasFunctions.cpp.

BoltzmanndndT()

double thermalfist::IdealGasFunctions::BoltzmanndndT	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Temperature derivatives.

Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-1].

Definition at line 1560 of file IdealGasFunctions.cpp.

BoltzmannEnergyDensity()

double thermalfist::IdealGasFunctions::BoltzmannEnergyDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the energy density of a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Energy density [GeV fm-3].

Definition at line 71 of file IdealGasFunctions.cpp.

BoltzmannEntropyDensity()

double thermalfist::IdealGasFunctions::BoltzmannEntropyDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the entropy density of a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Entropy density [GeV fm-3].

Definition at line 98 of file IdealGasFunctions.cpp.

BoltzmannMagnetization()

double thermalfist::IdealGasFunctions::BoltzmannMagnetization	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the thermal part of the magnetization of a Maxwell-Boltzmann gas, m_B = dP/dB.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.
extraConfig	Extra parameters such as magnetic field.

Returns

Magnetization [GeV^2].

Definition at line 1430 of file IdealGasFunctions.cpp.

BoltzmannPressure()

double thermalfist::IdealGasFunctions::BoltzmannPressure	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the pressure of a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Pressure [GeV fm-3].

Definition at line 66 of file IdealGasFunctions.cpp.

BoltzmannScalarDensity()

double thermalfist::IdealGasFunctions::BoltzmannScalarDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the scalar density of a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Scalar density [fm-3].

Definition at line 110 of file IdealGasFunctions.cpp.

BoltzmannTdndmu()

double thermalfist::IdealGasFunctions::BoltzmannTdndmu	(	int	N,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the chemical potential derivative of density for a Maxwell-Boltzmann gas.

Computes \( T \frac{\partial n}{\partial mu} \) for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( T \frac{\partial n}{\partial mu} \) [GeV fm-3].

Definition at line 137 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuChiN()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuChiN	(	int	N,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionless susceptibility for a Fermi-Dirac ideal gas at mu > m.

Computes \( \chi_n \equiv \frac{\partial^n p/T^4}{\partial (mu/T)^n} \) for a Fermi-Dirac ideal gas at mu > m.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 1174 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuChiNDimensionfull()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuChiNDimensionfull	(	int	N,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionfull susceptibility for a Fermi-Dirac ideal gas at mu > m.

Computes \( \chi_n \equiv \frac{\partial^n p}{\partial mu^n} \) for a Fermi-Dirac ideal gas at mu > m.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 1180 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMud2ndT2()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMud2ndT2	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the second derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-2].

Definition at line 1958 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMudchi2dT()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMudchi2dT	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dchi2dT [fm-3].

Definition at line 2049 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMudedmu()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMudedmu	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedmu [fm-3].

Definition at line 2018 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMudedT()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMudedT	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedT [fm-3].

Definition at line 1989 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuDensity()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the particle number density of a Fermi-Dirac ideal gas at mu > m.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Particle number density [fm-3].

Definition at line 927 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMudndT()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMudndT	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-1].

Definition at line 1929 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuEnergyDensity()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuEnergyDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the energy density of a Fermi-Dirac ideal gas at mu > m.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Energy density [GeV fm-3].

Definition at line 993 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuEntropyDensity()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuEntropyDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the entropy density of a Fermi-Dirac ideal gas at mu > m.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Entropy density [GeV fm-3].

Definition at line 1022 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuMagnetization()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuMagnetization	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1543 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuPressure()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuPressure	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the pressure of a Fermi-Dirac ideal gas at mu > m.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Pressure [GeV fm-3].

Definition at line 958 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuScalarDensity()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuScalarDensity	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the scalar density of a Fermi-Dirac ideal gas at mu > m.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Scalar density [fm-3].

Definition at line 1035 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuT1dn1dmu1()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuT1dn1dmu1	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1064 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuT2dn2dmu2()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuT2dn2dmu2	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1096 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuT3dn3dmu3()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuT3dn3dmu3	(	double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1126 of file IdealGasFunctions.cpp.

FermiNumericalIntegrationLargeMuTdndmu()

double thermalfist::IdealGasFunctions::FermiNumericalIntegrationLargeMuTdndmu	(	int	N,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1156 of file IdealGasFunctions.cpp.

FermiZeroTChiN()

double thermalfist::IdealGasFunctions::FermiZeroTChiN	(	int	N,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order susceptibility for a Fermi-Dirac ideal gas at zero temperature.

Computes \( \chi_n \equiv \frac{\partial^n p/T^4}{\partial (mu/T)^n} \) for a Fermi-Dirac ideal gas at mu > m.

Parameters

N	Susceptibility order.
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 1303 of file IdealGasFunctions.cpp.

FermiZeroTChiNDimensionfull()

double thermalfist::IdealGasFunctions::FermiZeroTChiNDimensionfull	(	int	N,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order susceptibility scaled by T^n for a Fermi-Dirac ideal gas at zero temperature.

Computes \( \chi_n \equiv \frac{\partial^n p}{\partial (mu)^n} \) for a Fermi-Dirac ideal gas at mu > m. Useful for zero temperature where the dimensionless susceptibility would be singular.

Parameters

N	Susceptibility order.
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \) [GeV^{4-N}].

Definition at line 1310 of file IdealGasFunctions.cpp.

FermiZeroTDensity()

double thermalfist::IdealGasFunctions::FermiZeroTDensity	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the particle number density of a Fermi-Dirac ideal gas at zero temperature.

Parameters

mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Particle number density [fm-3].

Definition at line 1186 of file IdealGasFunctions.cpp.

FermiZeroTdn1dmu1()

double thermalfist::IdealGasFunctions::FermiZeroTdn1dmu1	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1255 of file IdealGasFunctions.cpp.

FermiZeroTdn2dmu2()

double thermalfist::IdealGasFunctions::FermiZeroTdn2dmu2	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1265 of file IdealGasFunctions.cpp.

FermiZeroTdn3dmu3()

double thermalfist::IdealGasFunctions::FermiZeroTdn3dmu3	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1275 of file IdealGasFunctions.cpp.

FermiZeroTdndmu()

double thermalfist::IdealGasFunctions::FermiZeroTdndmu	(	int	N,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1285 of file IdealGasFunctions.cpp.

FermiZeroTEnergyDensity()

double thermalfist::IdealGasFunctions::FermiZeroTEnergyDensity	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the energy density of a Fermi-Dirac ideal gas at zero temperature.

Parameters

mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Energy density [GeV fm-3].

Definition at line 1213 of file IdealGasFunctions.cpp.

FermiZeroTEntropyDensity()

double thermalfist::IdealGasFunctions::FermiZeroTEntropyDensity	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the entropy density of a Fermi-Dirac ideal gas at zero temperature.

Parameters

mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Entropy density [GeV fm-3].

Definition at line 1231 of file IdealGasFunctions.cpp.

FermiZeroTMagnetization()

double thermalfist::IdealGasFunctions::FermiZeroTMagnetization	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 1553 of file IdealGasFunctions.cpp.

FermiZeroTPressure()

double thermalfist::IdealGasFunctions::FermiZeroTPressure	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the pressure of a Fermi-Dirac ideal gas at zero temperature.

Parameters

mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Pressure [GeV fm-3].

Definition at line 1195 of file IdealGasFunctions.cpp.

FermiZeroTScalarDensity()

double thermalfist::IdealGasFunctions::FermiZeroTScalarDensity	(	double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the scalar density of a Fermi-Dirac ideal gas at zero temperature.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Scalar density [fm-3].

Definition at line 1237 of file IdealGasFunctions.cpp.

GetSpins()

std::vector< double > thermalfist::IdealGasFunctions::GetSpins

(

double

degSpin

)

Calculate all the spin values -S, S+1,...,S-1,S.

Definition at line 28 of file IdealGasFunctions.cpp.

IdealGasQuantity()

double thermalfist::IdealGasFunctions::IdealGasQuantity	(	Quantity	quantity,
		QStatsCalculationType	calctype,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Calculation of a generic ideal gas function.

Calculations of the ideal gas thermodynamic function specified by

Parameters

quantity
quantity	Identifies the thermodynamic function to calculate.
calctype	Method used to perform the calculation if quantum statistics used.
statistics	0 – Maxwell-Boltzmann, +1 – Fermi-Dirac, -1 – Bose-Einstein.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.
order	Number of terms in the cluster expansion if this method is used.

Returns

Computed thermodynamic function.

Definition at line 1316 of file IdealGasFunctions.cpp.

psi()

double thermalfist::IdealGasFunctions::psi

(

double

x

)

Auxiliary function.

Auxiliary function used for Fermi-Dirac integrals at m > mu. See Eq. (A.2) in https://arxiv.org/pdf/0901.1430.pdf

Parameters

x

Variable.

Returns

Function value.

Definition at line 909 of file IdealGasFunctions.cpp.

psi2()

double thermalfist::IdealGasFunctions::psi2

(

double

x

)

Auxiliary function.

Auxiliary function used for Fermi-Dirac integrals at m > mu.

Parameters

x

Variable.

Returns

Function value.

Definition at line 918 of file IdealGasFunctions.cpp.

QuantumClusterExpansionChiN()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionChiN	(	int	N,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionless susceptibility for a quantum ideal gas using cluster expansion.

Computes \( \chi_n \equiv \frac{\partial^n p/T^4}{\partial (mu/T)^n} \) for a quantum ideal gas using cluster expansion.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 444 of file IdealGasFunctions.cpp.

QuantumClusterExpansionChiNDimensionfull()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionChiNDimensionfull	(	int	N,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionfull susceptibility for a quantum ideal gas using cluster expansion.

Computes \( \chi_n \equiv \frac{\partial^n p}{\partial mu^n} \) for a quantum ideal gas using cluster expansion.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \) [GeV^{4-N}].

Definition at line 452 of file IdealGasFunctions.cpp.

QuantumClusterExpansiond2ndT2()

double thermalfist::IdealGasFunctions::QuantumClusterExpansiond2ndT2	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the 2nd derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-2].

Definition at line 1646 of file IdealGasFunctions.cpp.

QuantumClusterExpansiondchi2dT()

double thermalfist::IdealGasFunctions::QuantumClusterExpansiondchi2dT	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dchi2dT [fm-3].

Definition at line 1739 of file IdealGasFunctions.cpp.

QuantumClusterExpansiondedmu()

double thermalfist::IdealGasFunctions::QuantumClusterExpansiondedmu	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedmu [fm-3].

Definition at line 1710 of file IdealGasFunctions.cpp.

QuantumClusterExpansiondedT()

double thermalfist::IdealGasFunctions::QuantumClusterExpansiondedT	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedT [fm-3].

Definition at line 1678 of file IdealGasFunctions.cpp.

QuantumClusterExpansionDensity()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the particle number density of a quantum ideal gas using cluster expansion.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Particle number density [fm-3].

Definition at line 155 of file IdealGasFunctions.cpp.

QuantumClusterExpansiondndT()

double thermalfist::IdealGasFunctions::QuantumClusterExpansiondndT	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-1].

Definition at line 1615 of file IdealGasFunctions.cpp.

QuantumClusterExpansionEnergyDensity()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionEnergyDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the energy density of a quantum ideal gas using cluster expansion.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Energy density [GeV fm-3].

Definition at line 265 of file IdealGasFunctions.cpp.

QuantumClusterExpansionEntropyDensity()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionEntropyDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the entropy density of a quantum ideal gas using cluster expansion.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Entropy density [GeV fm-3].

Definition at line 322 of file IdealGasFunctions.cpp.

QuantumClusterExpansionMagnetization()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionMagnetization	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the thermal part of the magnetization of a Maxwell-Boltzmann gas, m_B = dP/dB.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Magnetization [GeV^2].

Definition at line 1455 of file IdealGasFunctions.cpp.

QuantumClusterExpansionPressure()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionPressure	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the pressure of a quantum ideal gas using cluster expansion.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Pressure [GeV fm-3].

Definition at line 210 of file IdealGasFunctions.cpp.

QuantumClusterExpansionScalarDensity()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionScalarDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the scalar density of a quantum ideal gas using cluster expansion.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Scalar density [fm-3].

Definition at line 335 of file IdealGasFunctions.cpp.

QuantumClusterExpansionTdndmu()

double thermalfist::IdealGasFunctions::QuantumClusterExpansionTdndmu	(	int	N,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		int	order = 1,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the chemical potential derivative of density for a quantum ideal gas using cluster expansion.

Computes \( T \frac{\partial n}{\partial mu} \) for a quantum ideal gas using cluster expansion.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( T \frac{\partial n}{\partial mu} \) [GeV fm-3].

Definition at line 390 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationChiN()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationChiN	(	int	N,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionless susceptibility for a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Computes \( \chi_n \equiv \frac{\partial^n p/T^4}{\partial (mu/T)^n} \) for a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \).

Definition at line 888 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationChiNDimensionfull()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationChiNDimensionfull	(	int	N,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the n-th order dimensionfull susceptibility for a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Computes \( \chi_n \equiv \frac{\partial^n p}{\partial mu^n} \) for a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

N	Susceptibility order.
T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

\( \chi_n \) [GeV^{n-4}.

Definition at line 894 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationd2ndT2()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationd2ndT2	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the 2nd derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-2].

Definition at line 1803 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationdchi2dT()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationdchi2dT	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of the susceptibility wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dchi2dT [fm-3].

Definition at line 1895 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationdedmu()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationdedmu	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt mu at constant T for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedmu [fm-3].

Definition at line 1866 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationdedT()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationdedT	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of energy density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dedT [fm-3].

Definition at line 1837 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationDensity()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the particle number density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Particle number density [fm-3].

Definition at line 466 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationdndT()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationdndT	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the derivative of particle number density wrt T at constant mu for a Maxwell-Boltzmann gas.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

dndT [fm-3 * GeV^-1].

Definition at line 1771 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationEnergyDensity()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationEnergyDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the energy density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Energy density [GeV fm-3].

Definition at line 575 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationEntropyDensity()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationEntropyDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the entropy density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Entropy density [GeV fm-3].

Definition at line 629 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationMagnetization()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationMagnetization	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the magnetization of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Magnetization [GeV^2].

Definition at line 1501 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationPressure()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationPressure	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the pressure of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Pressure [GeV fm-3].

Definition at line 519 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationScalarDensity()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationScalarDensity	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Computes the scalar density of a quantum ideal gas using 32-point Gauss-Laguerre quadratures.

Parameters

T	Temperature [GeV].
mu	Chemical potential [GeV].
m	Particle's mass [GeV].
deg	Internal degeneracy factor.

Returns

Scalar density [fm-3].

Definition at line 645 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationT1dn1dmu1()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationT1dn1dmu1	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 698 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationT2dn2dmu2()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationT2dn2dmu2	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 753 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationT3dn3dmu3()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationT3dn3dmu3	(	int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 809 of file IdealGasFunctions.cpp.

QuantumNumericalIntegrationTdndmu()

double thermalfist::IdealGasFunctions::QuantumNumericalIntegrationTdndmu	(	int	N,
		int	statistics,
		double	T,
		double	mu,
		double	m,
		double	deg,
		const IdealGasFunctionsExtraConfig &	extraConfig = IdealGasFunctionsExtraConfig() )

Definition at line 868 of file IdealGasFunctions.cpp.

Variable Documentation

calculationHadBECIssue

bool thermalfist::IdealGasFunctions::calculationHadBECIssue = false

Whether \mu > m Bose-Einstein condensation issue was encountered for a Bose gas.

Definition at line 39 of file IdealGasFunctions.cpp.

lagw32

const double* thermalfist::IdealGasFunctions::lagw32 = NumericalIntegration::coefficients_wlag32

Definition at line 464 of file IdealGasFunctions.cpp.

lagx32

const double* thermalfist::IdealGasFunctions::lagx32 = NumericalIntegration::coefficients_xlag32

Definition at line 463 of file IdealGasFunctions.cpp.

legw32

const double* thermalfist::IdealGasFunctions::legw32 = NumericalIntegration::coefficients_wleg32_zeroone

Definition at line 461 of file IdealGasFunctions.cpp.

legx32

const double* thermalfist::IdealGasFunctions::legx32 = NumericalIntegration::coefficients_xleg32_zeroone

Definition at line 460 of file IdealGasFunctions.cpp.