On the irreversible nature of the Tsallis and Renyi entropies

Abstract We prove that the detailed balance hypothesis (i.e., Aij=Aji, where {Aij} are the transition probabilities, per unit time, between any two microscopic configurations i and j) implies irreversibility of both the recently introduced Tsallis entropy STq≡ [k/(q−1)](1−Σwi=1Pqi) as well as the Renyi entropy S R q ≡[k/(1−q)]ln(Σ w i=1 P q i )(qϵ R . More precisely, for q>0, Q=0and q