Variational methods in nonextensive Tsallis statistics: a comparative study

In the context of nonextensive Tsallis statistics, sensible examples are employed in order to compare the variational method proposed in Phys. Rev. Lett. 80 (1998) 218 with the one in J. Phys. A 26 (1993) L893. These examples are such that they can be solved exactly. Thus, a comparison of the exact result with the approximated ones is possible. The analysis of these examples indicates that the calculation related to the first variational method is easier to work with than the other method. In particular, when one is trying to apply the last variational method, the calculation of the approximated case can be more cumbersome than solving the exact one.