The Phase Space Elementary Cell in Classical and Generalized Statistics

Publisher： MDPI

E-ISSN： 1099-4300|15|10|4319-4333

ISSN： 1099-4300

Source： Entropy, Vol.15, Iss.10, 2013-10, pp. : 4319-4333

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Abstract

In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h 3 , at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger) phase-space volume described by non-extensive generalized statistics.