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

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

2000-06-19

arxiv.org/abs/cond-mat/0006279v2

Physics

Condensed Matter

Statistical Mechanics

Latex file. 11 pages. Sections 2 and 3 modified and shortened; an implicit assumption in Sec 4 is made explicit; a note and a

Scientific paper

10.1016/S0375-9601(00)00634-4

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.

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