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 effects, or a fractal-like relevant phase space, has raised interesting and profound issues concerning the properties of general thermostatistical formalisms. In the present paper we identify families of thermostatistical formalisms that share some fundamental characteristics. The canonical ensembleʹs invariance under uniform translations of the Hamiltonianʹs energy spectrum is shown to be a universal property verified by any thermostatistical formalism based upon linear mean energy constraints. We also provide multiparametric families of entropies exhibiting Tsallis q-additivity law.