Correct thermodynamic forces in Tsallis Thermodynamics: connection with Hill Nanothermodynamics

TL;DR

This paper establishes the equivalence between Tsallis Thermodynamics and Hill Nanothermodynamics, clarifies the correct thermodynamic forces, and derives a general expression for the entropic index q, relating it to system dynamics through examples.

Contribution

It demonstrates the equivalence between Tsallis Thermodynamics and Hill Nanothermodynamics and provides a new expression for q linked to Hamiltonian system dynamics.

Findings

Established the equivalence between Tsallis Thermodynamics and Hill Nanothermodynamics.

Identified the correct thermodynamic forces in Tsallis thermodynamics.

Derived a general expression for the entropic index q relating to system dynamics.

Abstract

The equivalence between Tsallis Thermodynamics and Hill Nanothermodynamics is established. The correct thermodynamic forces in Tsallis thermodynamics are pointed out. Through this connection we also find a general expression for the entropic index $q$ which we illustrate with two physical examples, allowing in both cases to relate $q$ to the underlying dynamics of the Hamiltonian systems.