Inertial Effects in Non-Equilibrium Thermodynamics

TL;DR

This paper explores inertial effects in non-equilibrium thermodynamics, deriving a unified framework that describes Brownian particles in both inertial and diffusive regimes using a mesoscopic approach.

Contribution

It introduces a Gibbs equation with entropy depending on probability density, unifying inertial and diffusion regimes in non-equilibrium thermodynamics.

Findings

Derived a relaxation equation for the diffusion current in inertial regime

Recovered Fick's law in the diffusion regime

Provided a mesoscopic description incorporating internal degrees of freedom

Abstract

We discuss inertial effects in systems outside equilibrium within the framework of non-equilibrium thermodynamics. By introducing a Gibbs equation in which the entropy depends on the probability density, we are able to describe a system of Brownian particles immersed in a heat bath in both inertial and diffusion regimes. In the former, a relaxation equation for the diffusion current is obtained whereas in the latter we recover Fick's law. Our approach, which uses the elements of the theory of internal degrees of freedom, constitutes the mesoscopic version of a previous analysis which takes into account the kinetic energy of diffusion.