Tsallis Statistics: Averages and a Physical Interpretation of the Lagrange Multiplier $β$

S. Kalyana Rama

doi:10.1016/S0375-9601(00)00634-4

paper

Tsallis Statistics: Averages and a Physical Interpretation of the Lagrange Multiplier $β$

arXiv:cond-mat/0006279 · doi:10.1016/S0375-9601(00)00634-4

Abstract

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 $β$ 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 $β$ , relating it to a physical temperature. We derive this interpretation by a different method also.

Latex file. 11 pages. Sections 2 and 3 modified and shortened; an implicit assumption in Sec 4 is made explicit; a note and a reference added; other minor changes. To appear in Physics Letters A

Tsallis Statistics: Averages and a Physical Interpretation of the Lagrange Multiplier β

Abstract

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Tsallis Statistics: Averages and a Physical Interpretation of the Lagrange Multiplier $β$