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Entropy 2013, 15(10), 4319-4333; doi:10.3390/e15104319
Article

The Phase Space Elementary Cell in Classical and Generalized Statistics

1,2,*  and 2
1 DISAT, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino I-10129, Italy 2 Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, Monserrato I-09042, Italy
* Author to whom correspondence should be addressed.
Received: 5 September 2013 / Revised: 25 September 2013 / Accepted: 27 September 2013 / Published: 15 October 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
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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, h3, 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.
Keywords: classical statistical mechanics; thermodynamics classical statistical mechanics; thermodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Quarati, P.; Lissia, M. The Phase Space Elementary Cell in Classical and Generalized Statistics. Entropy 2013, 15, 4319-4333.

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