Stationary state of a heated granular gas: fate of the usual H-functional

TL;DR

This paper investigates the nonequilibrium stationary state of a driven granular gas using entropy-based variational principles, examining stability and the applicability of different entropy measures.

Contribution

It introduces and evaluates entropy production candidates for characterizing the stationary state of a granular gas, highlighting the limitations of these approaches.

Findings

Neither entropy candidate shows an extremum at the stationary state.

The stability of the stationary state is analyzed under spatial homogeneity.

The relevance of the Kullback-Leibler entropy in this context is discussed.

Abstract

We consider the characterization of the nonequilibrium stationary state of a randomly-driven granular gas in terms of an entropy-production based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the non-equilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed.