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