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

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.

arXiv comment4 pages, 2 figures. v2: Some changes in text and new references added. arXiv admin note: text overlap with arXiv:2010.03357

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Cited by in corpus (1)

• Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag