Towards an $H$-theorem for granular gases

Abstract

The $H$-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium. As such, the theorem could not be generalized to account for dissipative systems: the conservative nature of collisions is an essential ingredient in the standard derivation. For a dissipative gas of grains, we construct here a simple functional $\mathcal{H}$ related to the original $H$, that can be qualified as a Lyapunov functional. It is positive, and results backed by three independent simulation approaches (a deterministic spectral method, the stochastic Direct Simulation Monte Carlo technique, and Molecular Dynamics) indicate that it is also non-increasing. Both driven and unforced cases are investigated.

References in corpus (5)

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• The Boltzmann equation for driven systems of inelastic soft spheres
• Entropy of continuous mixtures and the measure problem
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• Energy fluctuations in a randomly driven granular fluid

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• Information in feedback ratchets
• Mesoscopic description of the adiabatic piston: kinetic equations and $\mathcal{H}$-theorem
• Relative entropy of freely cooling granular gases. A molecular dynamics study