A Simple Model for the Entropy of a System With Interacting Particles

We present a simple model to calculate the system entropy of interacting particles where the interaction is modeled by unusual collisions concerning initial and final states. This model is based on the concept of dissipators to describe dissipative interactions between particles. Starting from the entropy of Clausius, we obtain expressions for the entropy of Boltzmann, Shannon and Tsallis. For this, we use a few simple rules related to the dissipaters in a kinetic model (e.g., average energy and the concept of statistical temperature in molecular theory). This work shows a possible explanation about the physical interpretation of parameter q in the Tsallis theory and the connection between the entropy of Tsallis and the entropy of Boltzmann-Shannon; under the concept of the dissipaters this theory does not exclude them since the way in which the energy is dissipated is in a certain way shared, these entropies belong to the same family of dissipators, to the powers of energy. The usual form of entropy is recovered according to the probability of phase-space, in terms of the energy density of the system.