Strong correlations between the exponent α and the particle number for a Renyi-monoatomic gas in Gibbs' statistical mechanics

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.