Quantum statistics of classical particles derived from the condition of a free diffusion coefficient

SISTERNA, P.; HOYUELOS, M.

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2016 vol. 94

1539-3755

We derive an equation for the current of particles in energy space; particles are subject to a mean-field effective potential that may represent quantum effects. From the assumption that noninteracting particles imply a free diffusion coefficient in energy space, we derive Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. Other new statistics are associated to a free diffusion coefficient; their thermodynamic properties are analyzed using the grand partition function. A negative relation between pressure and energy density for low temperatures can be derived, suggesting a possible connection with cosmological dark energy models.