Multicomponent Modified Boltzmann Equation and Thermalization

The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when – in contrast to the case of a single rule – several different composition rules are considered. The long-time behaviour of a simple momentum space model is explored numerically: saturating, heating and cooling solutions are presented.