Maximization of Tsallis entropy in the combinatorial formulation

This paper presents the mathematical reformulation for maximization of Tsallis entropy S_q in the combinatorial sense. More concretely, we generalize the original derivation of Maxwell-Boltzmann distribution law to Tsallis statistics by means of the corresponding generalized multinomial coefficient. Our results reveal that maximization of S_2−q under the usual expectation or S_q under q-average using the escort expectation are naturally derived from the combinatorial formulations for Tsallis statistics with respective combinatorial dualities, that is, one for additive duality and the other for multiplicative duality.