Statistical mechanics of granular gases in compartmentalized systems

We study the behavior of an assembly of N granular particles contained in two compartments within a simple kinetic approach. The particles belonging to each compartment collide inelastically with each other and are driven by a stochastic heat bath. In addition, the fastest particles can change compartment at a rate that depends on their kinetic energy. Via a Boltzmann velocity distribution approach, we first study the dynamics of the model in terms of a coupled set of equations for the populations in the containers and their granular temperatures and find a crossover from a symmetric high-temperature phase to an asymmetric low-temperature phase. Finally, in order to include statistical fluctuations, we solve the model within the direct simulation Monte Carlo approach. Comparisons with previous studies are presented.