Thermo-Statistical description of the Hamiltonian non extensive systems: The reparametrization invariance

TL;DR

This paper explores the reparametrization invariance in Hamiltonian nonextensive systems, proposing a geometric thermodynamic framework and revisiting phase transition classification, with insights from the Antonov model.

Contribution

It introduces the concept of reparametrization invariance as an internal symmetry in microcanonical ensembles, offering a new geometric approach to thermostatistics of nonextensive systems.

Findings

Reparametrization invariance acts as an internal symmetry in microcanonical ensembles.

A geometric formulation of thermodynamics based on this symmetry is proposed.

The classification of phase transitions is revised considering entropy concavity.

Abstract

In the present paper we continue our reconsideration about the foundations for a thermostatistical description of the called Hamiltonian nonextensive systems (see in cond-mat/0604290). After reviewing the selfsimilarity concept and the necessary conditions for the ensemble equivalence, we introduce the reparametrization invariance of the microcanonical description as an internal symmetry associated with the dynamical origin of this ensemble. Possibility of developing a geometrical formulation of the thermodynamic formalism based on this symmetry is discussed, with a consequent revision about the classification of phase-transitions based on the concavity of the Boltzmann entropy. The relevance of such conceptions are analyzed by considering the called Antonov isothermal model.