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Generalization of Boltzmann Equilibration Dynamics

We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study the influence of other interacting particles in terms of a random distortion of energy and momentum conservation occurring when multi-particle interactions are considered as binary collisions. Energy and momentum conservation still holds exactly but not in each model binary collision. We show how this new system differs from the Boltzmann system and we note that our approach naturally explains the emergence of Tsallis-like equilibrium statistics in physically relevant systems in terms of the long since neglected physics of interacting and dense systems.