Zeroth Law compatibility of non-additive thermodynamics

TL;DR

This paper identifies the general form of non-additive composition rules in non-extensive thermodynamics that are compatible with the Zeroth Law, potentially resolving longstanding issues in equilibrium between diverse thermodynamic systems.

Contribution

It derives the general functional form of non-additive rules compatible with the Zeroth Law, linking non-extensive and extensive thermodynamics through formal logarithms.

Findings

Non-additive composition rules can be made compatible with the Zeroth Law.

Formal logarithms transform non-additive rules into additive ones.

The results address equilibrium issues between systems with different non-extensivity parameters.

Abstract

Non-extensive thermodynamics was criticized among others by stating that the Zeroth Law cannot be satisfied with non-additive composition rules. In this paper we determine the general functional form of those non-additive composition rules which are compatible with the Zeroth Law of thermodynamics. We find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these. Our result offers a possible solution to the longstanding problem about equilibrium between extensive and non-extensive systems or systems with different non-extensivity parameters.