Tsallis statistics: averages and a physical interpretation of the Lagrangemultiplier beta

Tsallis has proposed a generalisation of the standard entropy, which has si nce been applied to a variety of physical systems. In the canonical ensembl e approach that is mostly used, average energy is given by an unnromalised, or normalised, q-expectation value. A Lagrange multiplier beta enforces th e energy constraint whose physical interpretation, however, is lacking. Her e, we use a microcanonical ensemble approach and find that consistency requ ires that only normalised q-expectation values are to be used. We then pres ent a physical interpretation of beta, relating it to a physical temperatur e. We derive this interpretation by a different method also. (C) 2000 Elsev ier Science B.V. All rights reserved.