The Tsallis Entropy and the Boltzmann Entropy Applicable to the Same Classical Generalized System

It is demonstrated clearly that for the same classical generalized system the Tsallis power-laws with both the 1 > q and the 1 < q can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithmetic mean for the generalized energies E . The author thus argues that there might be no definite “extensive system” or “classical system” and there are only “classical physical parameters” and “classical constraints”. For any physical system or generalized system, it is the non-natural constraints which determine both the forms of the entropies and the nonuniform equilibrium distributions. Keywords— Tsallis entropy, Boltzmann-Gibbs-Shannon entropy, extensive system, nonextensive systems, Tsallis power-law, Boltzmann distribution, Tsallis q-parameter.