Temperature of nonextensive system: Tsallis entropy as Clausius entropy

TL;DR

This paper explores the concept of temperature in nonextensive statistical mechanics, showing that Tsallis entropy can serve as Clausius entropy with a specific temperature definition, differing from previous notions.

Contribution

It demonstrates that the inverse Lagrange multiplier in Tsallis entropy acts as temperature, offering a new perspective on thermodynamics in nonextensive systems.

Findings

Tsallis entropy aligns with Clausius entropy under certain conditions

The temperature derived differs from the physical temperature previously proposed

Discussion on the role of Boltzmann's constant in generalized entropy systems

Abstract

The problem of temperature in nonextensive statistical mechanics is studied. Considering the first law of thermodynamics and a "quasi-reversible process", it is shown that the Tsallis entropy becomes the Clausius entropy if the inverse of the Lagrange multiplier, $beta$, associated with the constraint on the internal energy is regarded as the temperature. This temperature is different from the previously proposed "physical temperature" defined through the assumption of divisibility of the total system into independent subsystems. A general discussion is also made about the role of Boltzmann's constant in generalized statistical mechanics based on an entropy, which, under the assumption of independence, is nonadditive.