Phase Space Cell in Nonextensive Classical Systems

Abstract

We calculate the phase space volume $\Omega$ occupied by a nonextensive system of $N$ classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system) distribution function, which slightly deviates from Maxwell-Boltzmann (MB) distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change respect to the extensive MB case. We also derive, within a classical scheme, an analytical expression of the elementary cell that can be seen as a macrocell, different from the third power of Planck constant. Thermodynamic quantities like entropy, chemical potential and free energy of a classical ideal gas, depending on elementary cell, are evaluated. Considering the fractional deviation from MB distribution we can deduce a physical meaning of the nonextensive parameter $q$ of the Tsallis nonextensive thermostatistics in terms of particle correlation functions (valid at least in the case, discussed in this work, of small deviations from MB standard case). pacs: 05.20.-y, 05.70.-a keywords: Classical Statistical Mechanics, Thermodynamics