THERMODYNAMIC STABILITY CONDITIONS FOR THE TSALLIS AND RENYI ENTROPIES

Thermodynamic stability conditions (TSCs) are derived for the Tsallis and Renyi entropies. These entropies are monotononically increasing fu nctions of each other, so their TSCs are completely equivalent althoug h different in appearance. The TSC for the Renyi entropy S(q)R is simp ly that S(q)R be a concave (convex) function of the mean energy E for q > 0 (q < 0). This condition is not in general satisfied. The TSC for the Tsallis entropy S(q)T is then an immediate consequence of the non linear functional relation between S(q)T and S(q)R. Due to the nonline arity, the resulting TSC for S(q)T is not simply related to the concav ity (convexity) of S(q)T. The concavity properties of S(q)T are theref ore not sufficient to guarantee thermodynamic stability.