Entropy production in non-equilibrium fluctuating hydrodynamics

TL;DR

This paper investigates entropy production in non-equilibrium fluctuating hydrodynamics of granular fluids, expressing it through macroscopic quantities and analyzing its behavior across different models and length scales.

Contribution

It introduces a macroscopic expression for entropy production in fluctuating hydrodynamics of granular fluids, linking microscopic stochastic descriptions to thermodynamic quantities.

Findings

Entropy production is expressed as a product of thermodynamic force and current.

Entropy production vanishes in the elastic limit.

Different granular models exhibit qualitative differences in entropy production behavior.

Abstract

Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature and velocity), in the framework of model granular fluids. We find that the average entropy production, obtained from the microscopic stochastic description, can be expressed in terms of macroscopic quantities, in analogy with linear non-equilibrium thermodynamics. We consider the specific cases of driven granular fluids with two different kinds of thermostat and the homogeneous cooling regime. In all cases, the average entropy production turns out to be the product of a thermodynamic force and a current: the former depends on the specific energy injection mechanism, the latter takes always the form of a static correlation between fluctuations of density and temperature time-derivative. Both vanish in the elastic limit. The behavior of the entropy production is studied at different length scales and the qualitative differences arising for the different granular models are discussed.