H-THEOREMS FOR THE TSALLIS AND RENYI ENTROPIES

Mariz [Phys. Lett. A 165 (1992) 409] recently analyzed the time evolution of the Tsallis entropy S(q)T and the Renyi entropy S(q)R based on the master equation and the assumption of detailed balance. Mariz restricted attention to situations where the equilibrium probability distribution is uniform, for which he showed that dS(q)T/dt and dS(q)R/dt have the same sign as the parameter q. Here we show that these results continue to hold in the absence of detailed balance. We also present the generalization to cases with nonuniform equilibrium distributions, for which it is necessary to appropriately redefine the entropy relative to equilibrium.