Zeroth law of thermodynamics and the transformation from nonextensive to extensive framework

TL;DR

This paper explores how the zeroth law of thermodynamics governs the relationship between nonextensive and extensive entropy frameworks, revealing how different constraints influence the form of entropy and the mapping of thermodynamic variables.

Contribution

It demonstrates the role of the zeroth law in connecting nonextensive and extensive entropies and clarifies how constraints determine the resulting entropy form.

Findings

Standard averages lead to Boltzmann-Shannon-Gibbs entropy.

Normalized biased averages lead to Renyi entropy.

The mapping between Lagrange multipliers and intensive variables is generalized.

Abstract

Within the nonextensive framework, it is shown that zeroth law of thermodynamics determines not only the mapping between Lagrange multipliers and intensive variables, but also the mapping between nonextensive and extensive entropy. The form of constraints decides the form of the extensive entropy, standard averages lead to Boltzmann-Shannon-Gibbs entropy while normalised biased averages lead to Renyi entropy. The mapping between Lagrange multipliers and intensive variables is also discussed in the more general context of composable entropy.