On the thermodynamics of classical micro-canonical systems

TL;DR

This paper investigates the thermodynamics of finite classical systems in the micro-canonical ensemble, arguing that Renyi's entropy better describes the configurational subsystem's thermodynamics than Tsallis entropy.

Contribution

It provides two theoretical arguments supporting the use of Renyi's entropy over Tsallis entropy for the configurational subsystem in micro-canonical systems.

Findings

Renyi's entropy aligns with the temperature of the kinetic subsystem.

The instability of the pendulum near the rotation threshold is accurately modeled.

The thermodynamic behavior of finite systems is better captured by Renyi's entropy.

Abstract

We study the configurational probability distribution of a mono-atomic gas with a finite number of particles N in the micro-canonical ensemble. We give two arguments why the thermodynamic entropy of the configurational subsystem involves Renyi's entropy function rather than that of Tsallis. The first argument is that the temperature of the configurational subsystem is equal to that of the kinetic subsystem. The second argument is that the instability of the pendulum, which occurs for energies close to the rotation threshold, is correctly reproduced.