Non-additivity of Tsallis entropies and fluctuations of temperature

We show that the non-additivity relation of the Tsallis entropies in nonextensive statistical mechanics has a simple physical interpretation for systems with fluctuating temperature or fluctuating energy dissipation rate. We also show that there is a distinguished dependence of the entropic index q on the spatial scale that makes the Tsallis entropies quasi-additive. Quasi-additivity implies that q is a strictly monotonously decreasing function of the spatial scale r, as indeed observed in various experiments. 1 permanent address: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS. The formalism of nonextensive statistical mechanics has been developed over the past 13 years as a powerful and beautiful generalization of ordinary statistical mechanics [1]–[4]. It is based on the extremization of the Tsallis entropies Sq = 1 q − 1 (