Class StatisticalDistributions

java.lang.Object
org.episteme.natural.physics.statistical.StatisticalDistributions
public class StatisticalDistributions extends Object
Statistical distribution functions for particles.

Provides implementations for:

  • Maxwell-Boltzmann (classical)
  • Fermi-Dirac (fermions)
  • Bose-Einstein (bosons)

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Field Details

    • K_B

      public static final Real K_B

  • Constructor Details

    • StatisticalDistributions

      public StatisticalDistributions()

  • Method Details

    • maxwellBoltzmann

      public static Real maxwellBoltzmann(Real energy, Real temperature)
      Maxwell-Boltzmann distribution: $f(E) = A \exp(-E / k_B T)$ Returns UNNORMALIZED probability.

    • fermiDirac

      public static Real fermiDirac(Real energy, Real chemicalPotential, Real temperature)
      Fermi-Dirac distribution: $f(E) = 1 / (\exp((E - \mu) / k_B T) + 1)$ Chemical potential $\mu$ is often the Fermi energy at T=0.

    • boseEinstein

      public static Real boseEinstein(Real energy, Real chemicalPotential, Real temperature)
      Bose-Einstein distribution: $f(E) = 1 / (\exp((E - \mu) / k_B T) - 1)$ For photons/phonons, $\mu = 0$.

    • partitionFunction

      public static Real partitionFunction(Real[] energyLevels, Real temperature)
      Partition function for a system with discrete energy levels. $Z = \sum_i \exp(-E_i / k_B T)$