The Phase Space Elementary Cell in Classical and Generalized Statistics

TL;DR

This paper explores how the phase space volume and elementary cell size in classical and generalized statistics change with interactions and correlations, challenging traditional assumptions and linking to cosmological implications.

Contribution

It derives expressions for phase space volume and elementary cell size in correlated systems and connects these to cosmological and astrophysical phenomena.

Findings

Elementary cell volume need not be fixed at h^3 in non-quantized systems.

Interactions and correlations alter the phase space volume and number of states.

Different effective phase-space volumes relate to non-extensive generalized statistics.

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.