Critique of multinomial coefficients method for evaluating Tsallis and Renyi entropies

TL;DR

This paper critically examines a method using generalized multinomial coefficients for calculating Tsallis and Renyi entropies, revealing errors and misconceptions in previous work and clarifying the correct approach.

Contribution

It demonstrates that the multinomial coefficients method fails for Tsallis entropy and corrects errors in prior analysis, clarifying the proper understanding of these entropies.

Findings

The multinomial coefficients method does not correctly determine Tsallis entropy at equilibrium.

Oikonomou's analysis contains mistakes leading to misleading conclusions.

The paper clarifies the correct relationship between generalized multinomial coefficients and entropy calculations.

Abstract

Oikonomou [Physica A 386 (2007) 119] has published a calculation which purports to show that the Tsallis and Renyi entropies can be obtained from the generalized multinomial coefficients. In this paper, we prove that the method of generalized multinomial coefficients failed to determine the Tsallis entropy at equilibrium. Moreover, it is shown that Oikonomou's analysis contains mistakes which led him to misleading statements related to the Jaynes principle of maximum entropy, the Tsallis and the Renyi statistics.