Towards an $H$-theorem for granular gases

M. I. García De Soria 1 P. Maynar 1 S. Mischler 2 C. Mouhot 3 T. Rey 4 E. Trizac 5

Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2015, pp.P11009

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.

• 1. Fisica Teorica, Universidad de Sevilla
• 2. CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
• 3. DPMMS/CMS
• 4. LPP - Laboratoire Paul Painlevé
• 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques