Basic-deformed thermostatistics

TL;DR

This paper introduces a q-deformed statistical mechanics framework based on the basic-exponential, leading to a natural energy cut-off and preserving thermodynamic relationships, with potential applications to systems with long-range interactions.

Contribution

It formulates a generalized statistical mechanics using basic-hypergeometric series and q-calculus, extending thermostatistics with a natural energy cut-off and maintained thermodynamic structure.

Findings

Distribution exhibits a natural energy cut-off.

Standard thermodynamic relationships are preserved.

Framework reduces to ordinary thermostatistics at q=1.

Abstract

Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a q-nonuniform lattice we introduce the basic-entropy related to the basic-exponential by means of a q-variational principle. Remarkably, this distribution exhibits a natural cut-off in the energy spectrum. This fact, already encountered in other formulations of generalized statistical mechanics, is expected to be relevant to the applications of the theory to those systems governed by long-range interactions. By employing the q-calculus, it is shown that the standard thermodynamic functional relationships are preserved, mimicking, in this way, the mathematical structure of the ordinary thermostatistics which is recovered in the q=1 limit.