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

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