On the definition of temperature using time--averages

TL;DR

This paper redefines temperature in statistical thermodynamics using Caratheodory's approach, coupling systems to heat baths, and derives an additive form of Tsallis entropy, challenging conventional views.

Contribution

It introduces a new definition of temperature based on heat exchange and derives an additive form of Tsallis entropy, contrasting with traditional non-additive interpretations.

Findings

Temperature defined as an integrating factor of exchanged heat.

Derived an additive form of Tsallis entropy.

Established a consistent thermodynamic framework far from equilibrium.

Abstract

This paper is a natural continuation of a previous one by the author, which was concerned with the foundations of statistical thermodynamics far from equilibrium. One of the problems left open in that paper was the correct definition of temperature. In the literature, temperature is in general defined through the mean kinetic energy of the particles of a given system. In this paper, instead, temperature is defined "a la Caratheodory", the system being coupled to a heat bath, and temperature being singled out as the ``right'' integrating factor of the exchanged heat. As a byproduct, the ``right'' expression for the entropy is also obtained. In particular, in the case of a q-distributions the entropy turns out to be that of Tsallis, which we however show to be additive, at variance with what is usually maintained.