Rp. Di Sisto et al., General thermostatistical formalisms, invariance under uniform spectrum translations, and Tsallis q-additivity, PHYSICA A, 265(3-4), 1999, pp. 590-613
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.