Tsallis statistics:: averages and a physical interpretation of the Lagrange multiplier β

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