General thermostatistical formalisms, invariance under uniform spectrum translations, and Tsallis q-additivity

The recent proposal by Tsallis of a generalized thermostatistics devised to treat systems endowed with long-range interactions, long-range memory effe cts, or a fractal-like relevant phase space, has raised interesting and pro found issues concerning the properties of general thermostatistical formali sms. In the present paper we identify families of thermostatistical formali sms that share some fundamental characteristics, The canonical ensemble's i nvariance under uniform translations of the Hamiltonian's energy spectrum i s shown to be a universal property verified by any thermostatistical formal ism based upon linear. mean energy constraints. We also provide multiparame tric families of entropies exhibiting Tsallis q-additivity law. (C) 1999 El sevier Science B.V. All rights reserved.