  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.
