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

TL;DR

This paper explores how ballistic transport affects thermodynamic properties, revealing non-Gaussian behavior, non-ergodicity, and entropy anomalies across different diffusion regimes, challenging classical statistical assumptions.

Contribution

It provides a comprehensive analysis of ballistic diffusion with colored noise, highlighting non-Gaussian distributions and entropy behavior, extending understanding beyond standard diffusion models.

Findings

Entropy does not reach a maximum in ballistic diffusion.

Non-Gaussian behavior occurs, violating the central limit theorem.

The second law of thermodynamics is preserved despite non-ergodicity.

Abstract

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