Relative entropy of freely cooling granular gases. A molecular dynamics study

TL;DR

This study uses molecular dynamics simulations to investigate the relative entropy of velocity distributions in freely cooling granular gases, supporting the conjecture that it serves as an appropriate nonequilibrium entropy measure.

Contribution

It provides empirical evidence from molecular dynamics that supports the use of relative entropy with respect to the homogeneous cooling state as a nonequilibrium entropy functional for granular gases.

Findings

Relative entropy aligns with the HCS as a reference distribution.

Maxwellian distribution is less suitable than HCS.

Microscopic irreversibility is observed through a Maxwell-demon-like experiment.

Abstract

Whereas the original Boltzmann's $H$-theorem applies to elastic collisions, its rigorous generalization to the inelastic case is still lacking. Nonetheless, it has been conjectured in the literature that the relative entropy of the velocity distribution function with respect to the homogeneous cooling state (HCS) represents an adequate nonequilibrium entropy-like functional for an isolated freely cooling granular gas. In this work, we present molecular dynamics results reinforcing this conjecture and rejecting the choice of the Maxwellian over the HCS as a reference distribution. These results are qualitatively predicted by a simplified theoretical toy model. Additionally, a Maxwell-demon-like velocity-inversion simulation experiment highlights the microscopic irreversibility of the granular gas dynamics, monitored by the relative entropy, where a short ``anti-kinetic'' transient regime appears for nearly elastic collisions only.