February 3, at 3 PM - GSSI Main Lecture Hall

Angelo Vulpiani, Professor of Theoretical Physics, University Roma Sapienza

Abstract

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term.

Such a non-linear equation describing the evolution of the single particle probability of being in given state at time t, is a suitable model for granular gases and is indicated here as Boltzmann-Fokker-Planck (BFP) equation.

The conjectured H-functional, which appears to be non-increasing, is the Kullback-Leibler divergence, in analogy with the H-functional of Markov processes.

A simple proof can be given for the elastic BFP equation.

A semi-analytical proof is also offered for the BFP equation for so-called inelastic Maxwell molecules. Other evidence is obtained by solving particular BFP cases through numerical integration or through "particle schemes" such as the Direct Simulation Monte Carlo.