ON THE IRREVERSIBLE NATURE OF THE TSALLIS AND RENYI ENTROPIES

We prove that the detailed balance hypothesis (i.e., A(ij)=A(ji), where {A(ij)} are the transition probabilities, per unit time, between any two microscopic configurations i and j) implies irreversibility of both the recently introduced Tsallis entropy S(q)T=[k/(q-1)] (1-SIGMA-(i=1)w P(i)q) as well as the Renyi entropy S(q)R=[k/(1-q)]ln(SIGMA-(i=1)w P(i)q (q is-an-element-of R). More precisely, for q>0, q=0 and q<0 we have respectively dS/dt greater-than-or-equal-to 0, dS/dt=0 and dS/dt less-than-or-equal-to 0 (S=S(q)T, S(q)R), where the equality holds for equilibrium.