Non-additivity of Tsallis entropies and fluctuations of temperature

Isaac Newton Institute for Mathematical Sciences, University of Cambridge 20 Clarkson Road, Cambridge CB3 0EH, UK

Received: 30 April 2001
Accepted: 12 November 2001

Abstract

We show that the nonadditivity 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.