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The Phase Space Elementary Cell in Classical and Generalized Statistics
DISAT, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino I-10129, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, Monserrato I-09042, Italy
* Author to whom correspondence should be addressed.
Received: 5 September 2013; in revised form: 25 September 2013 / Accepted: 27 September 2013 / Published: 15 October 2013
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
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MDPI and ACS Style
Quarati, P.; Lissia, M. The Phase Space Elementary Cell in Classical and Generalized Statistics. Entropy 2013, 15, 4319-4333.
Quarati P, Lissia M. The Phase Space Elementary Cell in Classical and Generalized Statistics. Entropy. 2013; 15(10):4319-4333.
Quarati, Piero; Lissia, Marcello. 2013. "The Phase Space Elementary Cell in Classical and Generalized Statistics." Entropy 15, no. 10: 4319-4333.