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
Highlights
Statistical description of a system of N particles requires the subdivision of the phase space into equidimensional elementary cells of phase volume ∆Ω, which can be determined by the laws of nature and experimentally measured, for instance, in the low temperature heat capacity of a crystal or in the Stefan-Boltzmann constant.In the phase space volume of a system of particles described by quantum distribution the smallest elementary cell is the third power of the Planck constant
This paper aims at examing first of all how, in the nonextensive thermostatistics (NETS), the elementary cell differs from the one of the extensive MB case, requiring explicitly that the number of accessible microstates be the same in both phase spaces and obtain within a classical scheme and without quantum arguments, explicit expressions of the cells
Classical ideal gas model based on nonextensive thermostatistics relations has been the subject of several studies since the first applications of NETS [24, 25].Classical ideal gas is described by an unperturbed state of a system with long-range interaction and the model can be solved analytically
Summary
Statistical description of a system of N particles requires the subdivision of the phase space into equidimensional elementary cells of phase volume ∆Ω, which can be determined by the laws of nature (comparison with quantum evaluation of energy state density) and experimentally measured, for instance, in the low temperature heat capacity of a crystal or in the Stefan-Boltzmann constant. For classical particles the elementary cell is, in principle, undetermined This is true in the limiting case of small occupation numbers (when MB distribution is valid) and the phase space volume of a cell acquires arbitrary values. This paper aims at examing first of all how, in the nonextensive thermostatistics (NETS), the elementary cell differs from the one of the extensive MB case, requiring explicitly that the number of accessible microstates be the same in both (extensive and nonextensive) phase spaces and obtain within a classical scheme and without quantum arguments, explicit expressions of the cells. The approach to NETS we are showing in this paper, is based on the analysis of deviations from standard phase space volume and on a new definition of elementary cell This new approach will probabily provide, in the near future, a better understanding of the meaning of the parameter q.
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