Computer simulation of effective potentials for generalized Boltzmann-Gibbs statistics

We consider a previously proposed non-extensive Statistical Mechanics approach based on an entropy expression that does not depend on any parameter and it is only given in terms of the probability distribution, as in the Boltzmann-Gibbs (BG) case. The theory reproduces the BG theory in a well defined limit. In this article we demonstrate that the theory is consistent with the existence of a generalized H-theorem. The corresponding H function is given in terms of the Maxwellian state, and a generalized version of the ideal gas model can be derived. For denser systems, we present predictions obtained by Monte Carlo computer simulations for fluids whose particles interact via square-well (SW) or Lennard-Jones (LJ) potentials. Results allow us to obtain a well-defined mapping between the BG and non-extensive Statistical Mechanics theories through the introduction of an effective potential of mean force. Using this effective potential, effective Boltzmann factors can be defined in order to obtain non-extensive thermodynamic properties within the BG framework. We discuss how this mapping resemblances an analogy with the definition of Slater sums in Quantum Statistical Mechanics.