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

TL;DR

This paper derives quantum statistical distributions from a classical diffusion framework influenced by a mean field potential, revealing new insights into particle behavior and potential cosmological implications.

Contribution

It introduces a novel derivation of quantum statistics from classical diffusion principles, linking thermodynamics and cosmology.

Findings

Derivation of Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics from diffusion assumptions.

Identification of new statistics associated with a free diffusion coefficient.

Discovery of a negative pressure-energy relation at low temperatures, hinting at dark energy connections.

Abstract

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 non-interacting 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.