Class StatisticalMechanics

java.lang.Object

org.episteme.natural.physics.StatisticalMechanics

public class StatisticalMechanics
extends Object

Statistical mechanics - bridge between microscopic and macroscopic physics.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
StatisticalMechanics()

Method Summary

Modifier and Type	Method	Description
static Real	averageEnergy(Real partitionFunction, Real temperature, Real dZdT)	Average energy from partition function
static Real	boltzmannEntropy(Real numMicrostates)	Boltzmann entropy: S = k ln(Ω)
static Real	boltzmannProbability(Real energy, Real temperature, Real partitionFunction)	Boltzmann distribution: P(E) = e^(-E/kT) / Z
static Real	boseEinsteinDistribution(Real energy, Real chemicalPotential, Real temperature)	Bose-Einstein distribution: f(E) = 1/(e^((E-μ)/kT) - 1)
static Real	fermiDiracDistribution(Real energy, Real chemicalPotential, Real temperature)	Fermi-Dirac distribution: f(E) = 1/(e^((E-μ)/kT) + 1)
static Real	gibbsFreeEnergy(Real enthalpy, Real temperature, Real entropy)	Gibbs free energy: G = H - TS
static Real	heatCapacity(Real dEnergyDT)	Heat capacity: C = ∂/∂T
static Real	helmholtzFreeEnergy(Real internalEnergy, Real temperature, Real entropy)	Helmholtz free energy: F = U - TS
static Real	maxwellBoltzmannSpeed(Real speed, Real mass, Real temperature)	Maxwell-Boltzmann speed distribution
static Real	partitionFunction(Vector<Real> energies, Real temperature)	Partition function: Z = Σᵢ e^(-Eᵢ/kT)

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

StatisticalMechanics

public StatisticalMechanics()

Method Details

boltzmannProbability

public static Real boltzmannProbability(Real energy,
 Real temperature,
 Real partitionFunction)

Boltzmann distribution: P(E) = e^(-E/kT) / Z

partitionFunction

public static Real partitionFunction(Vector<Real> energies,
 Real temperature)

Partition function: Z = Σᵢ e^(-Eᵢ/kT)

boltzmannEntropy

public static Real boltzmannEntropy(Real numMicrostates)

Boltzmann entropy: S = k ln(Ω)

maxwellBoltzmannSpeed

public static Real maxwellBoltzmannSpeed(Real speed,
 Real mass,
 Real temperature)

Maxwell-Boltzmann speed distribution

averageEnergy

public static Real averageEnergy(Real partitionFunction,
 Real temperature,
 Real dZdT)

Average energy from partition function

heatCapacity

public static Real heatCapacity(Real dEnergyDT)

Heat capacity: C = ∂/∂T

fermiDiracDistribution

public static Real fermiDiracDistribution(Real energy,
 Real chemicalPotential,
 Real temperature)

Fermi-Dirac distribution: f(E) = 1/(e^((E-μ)/kT) + 1)

boseEinsteinDistribution

public static Real boseEinsteinDistribution(Real energy,
 Real chemicalPotential,
 Real temperature)

Bose-Einstein distribution: f(E) = 1/(e^((E-μ)/kT) - 1)

gibbsFreeEnergy

public static Real gibbsFreeEnergy(Real enthalpy,
 Real temperature,
 Real entropy)

Gibbs free energy: G = H - TS

helmholtzFreeEnergy

public static Real helmholtzFreeEnergy(Real internalEnergy,
 Real temperature,
 Real entropy)

Helmholtz free energy: F = U - TS