Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanics

Details Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanics Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanics

2002-03-26

arxiv.org/abs/cond-mat/0203536v2

Physics

Condensed Matter

Statistical Mechanics

17 pages, Latex. Revised version, clarifications on mean field. Part of this work was presented as a talk at NEXT2001- Non-Ext

Scientific paper

I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous thermo--statistical--geometrical formalisms, (pseudo-)Riemannian [Weinhold 1975; Ruppeiner 1979] as well as Euclidean [Gilmore 1984; Gross& Votyakov 1999] or Euclidean--looking [Levine 1986]. I point out the relevance of this approach within the contexts of non--extensive statistical thermodynamics [Tsallis 1988, 2000]. I show how the language of Riemannian geometry can be used as a powerful investigation tool,leading to several new and profound questions, and some temptative answers, on thermo--statistical mechanics.

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