Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport

Abstract

Ballistic transportation introduces new challenges in the thermodynamic\nproperties of a gas of particles. For example, violation of mixing, ergodicity\nand of the fluctuation-dissipation theorem may occur, since all these processes\nare connected. In this work, we obtain results for all ranges of diffusion,\ni.e., both for subdiffusion and superdiffusion, where the bath is such that it\ngives origin to a colored noise. In this way we obtain the skewness and the\nnon-Gaussian factor for the probability distribution function of the dynamical\nvariable. We put particular emphasis on ballistic diffusion, and we demonstrate\nthat in this case, although the second law of thermodynamics is preserved, the\nentropy does not reach a maximum and a non-Gaussian behavior occurs. This\nimplies the non-applicability of the central limit theorem.\n