Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanics
Abstract
Description
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.
17 pages, Latex. Revised version, clarifications on mean field. Part of this work was presented as a talk at NEXT2001- Non-Extensive Thermodynamics and Physical Applications, Villasimius, Italy, but NOT included in the proceedings (Physica A 305, 84-88, 2002); G.Kaniadakis suggested me to make the present work available on line. Figures at http://www.ca.infn.it/~lissia/next2001/lucidi/trasarti-battistoni
17 pages, Latex. Revised version, clarifications on mean field. Part of this work was presented as a talk at NEXT2001- Non-Extensive Thermodynamics and Physical Applications, Villasimius, Italy, but NOT included in the proceedings (Physica A 305, 84-88, 2002); G.Kaniadakis suggested me to make the present work available on line. Figures at http://www.ca.infn.it/~lissia/next2001/lucidi/trasarti-battistoni