Microcanonical equations for the Tsallis entropy

TL;DR

This paper derives microcanonical thermodynamic equations based on Tsallis entropy, compares two temperature definitions, and discusses implications for ideal gases and thermodynamic laws.

Contribution

It introduces microcanonical equations for Tsallis entropy and compares two temperature definitions, including a 'physical' one satisfying the zeroth law.

Findings

The 'physical' temperature satisfies the zeroth law.

Results for ideal gases align with canonical results.

Most formulae remain unchanged from extensive thermodynamics.

Abstract

Microcanonical equations for several thermodynamic properties of a system, suitable for molecular dynamics simulations, are derived from the nonextensive Tsallis entropy functional. Two possible definitions of temperature, the usual one and a ``physical'' modification which satisfies the zeroth law of thermodynamics, are considered, and the results from both choices are compared. Results for the ideal gas using the first definition of temperature are provided and discussed in relation with the canonical results reported in the literature. The second choice leaves most formulae unchanged from their extensive (Shannon-Boltzmann-Gibbs) form.