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.