Energy distribution of inelastic gas in a box is dominated by a power law - a derivation in the framework of sample space reducing processes

We use the framework of sample space reducing (SSR) processes as an alternative to Boltzmann equation based approaches to derive the energy and velocity distribution functions of an inelastic gas in a box as an example of a dissipative, driven system. SSR processes do not assume molecular chaos and are characterized by a specific type of eigenvalue equation whose solutions represent stationary distribution functions. The equations incorporate the geometry of inelastic collisions and a driving mechanism in a transparent way. Energy is injected by boosting particles that hit the walls of the container to high energies. The numerical solution of the resulting equations yields approximate power laws over the entire energy region. The exponents decrease with the driving rate from about 2 to below 1.5 and depend on the coefficient of restitution. Results are confirmed with a molecular dynamics simulation in 3D with the same driving mechanism. The numerical solution of the resulting equations yields approximate power laws over the entire energy region. Deviations depend on the details of driving, density, and container.