The Phase Space Elementary Cell in Classical and Generalized Statistics
arXiv:1501.04463 · doi:10.3390/e15104319
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.
15 pages, no figures. Published in Entropy 2013, 15, 4319-4333
References in corpus (13)
- The fundamental constants and their variation: observational status and theoretical motivations
- Statistical mechanics in the context of special relativity
- Indications of a spatial variation of the fine structure constant
- Sub-Planck spots of Schroedinger cats and quantum decoherence
- Formulation of the uncertainty relations in terms of the Renyi entropies
- Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
- Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
- Uncertainty relations in terms of Tsallis entropy
- Essential discreteness in generalized thermostatistics with non-logarithmic entropy
- Generalized thermodynamic uncertainty relations
- Reply to the Comment by B. Andresen
- Classical Equilibrium Thermostatistics, "Sancta sanctorum of Statistical Mechanics", From Nuclei to Stars
- Phase Space Cell in Nonextensive Classical Systems