Possible Force-Entropy Correlation

TL;DR

This paper presents a statistical thermodynamic approach linking force and entropy in elastic systems, deriving classical and nonextensive entropy forms and relating them to mechanical laws.

Contribution

It introduces a novel connection between force and entropy, deriving both Boltzmann-Gibbs and Tsallis entropy forms within a unified framework.

Findings

Derivation of Boltzmann-Gibbs entropy from mechanical principles

Extension to Tsallis nonextensive entropy with a proportional thermal energy assumption

Relation of entropy forms to Newton's law of motion

Abstract

A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy form and relate it to Newton's law of motion in relation to a distinct tensile force acting on the systems at constant volume and number of particles. Tsallis generalization of the BG entropy is deduced assuming the thermal energy of the particles to be proportional to their energy states by the nonextensivity factor q-1.