q-deformed structures and generalized thermodynamics

TL;DR

This paper explores how q-calculus can be used to develop a generalized thermodynamics framework based on q-deformed algebra, preserving thermodynamic structure and extending classical dynamics.

Contribution

It introduces a q-calculus-based formalism for q-deformed thermodynamics and proposes a q-deformation of the classical Poisson bracket for generalized dynamics.

Findings

Thermodynamics structure is preserved with Jackson derivative.

Q-deformation of classical Poisson brackets is proposed.

Formalism extends to classical and quantum regimes.

Abstract

On the basis of the recently proposed formalism [A. Lavagno and P.N. Swamy, Phys. Rev. E 65, 036101 (2002)], we show that the realization of the thermostatistics of q-deformed algebra can be built on the formalism of q-calculus. It is found that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative instead of the ordinary thermodynamic derivative. Furthermore, in analogy with the quantum q-oscillator algebra, we also investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized q-deformed dynamics in the classical regime.