Relative Entropy of a Freely Cooling Granular Gas

TL;DR

This paper investigates the entropy evolution of a freely cooling granular gas, revealing complex dependencies on restitution coefficients and a unique behavior in the quasi-smooth limit through a Sonine approximation.

Contribution

It introduces a detailed analysis of the relative entropy dynamics in granular gases using a Sonine approximation with fourth-degree cumulants, highlighting novel behaviors.

Findings

Relative entropy depends intricately on restitution coefficients.

Distinct behavior observed in the quasi-smooth limit.

Rich variety of entropy evolution patterns identified.

Abstract

The time evolution and stationary values of the entropy per particle of a homogeneous freely cooling granular gas, relative to the maximum entropy consistent with the instantaneous translational and rotational temperatures, is analyzed by means of a Sonine approximation involving fourth-degree cumulants. The results show a rich variety of dependencies of the relative entropy on time and on the coefficients of normal and tangential restitution, including a peculiar behavior in the quasi-smooth limit.