# Strong correlations between the exponent $\alpha$ and the particle number for a Renyi-monoatomic gas in Gibbs' statistical mechanics

## TL;DR

This paper demonstrates a strong correlation between Renyi's exponent and particle number in classical statistical mechanics systems, using Gibbs' axiomatic framework without involving heat baths.

## Contribution

It reveals a novel classical correlation between Renyi's exponent and particle number, independent of heat bath references, within Gibbs' formalism.

## Key findings

- Strong correlation between $oldsymbol{ ext{α}}$ and particle number
- Correlation observed without heat bath involvement
- Applicable to simple classical systems

## Abstract

Appealing to the 1902 Gibbs' formalism for classical statistical mechanics (SM), the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics, we will here show that already at the classical level there is a strong correlation between the Renyi's exponent $\alpha$ and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.