Non extensive thermostatistics and complex systems

Standard statistical mechanics is extensive, i.e. the Boltzmann-Gibbs entropy of two subsets of a gas is just the sum of the two because of the short-range nature of the interaction. But many objects in Nature interact through long-range interactions, think of gravitational or unscreened Coulomb forces. Therefore the property of additivity is very often violated. This is simply forgotten in standards thermostatistics books apart from some sentences of warning in the very first pages. In order to take this fact into account, Constantino Tsallis in 1988, proposed a new formula for the entropy which is non extensive and contains the standard Boltzmann-Gibbs one as a limiting case. In the last decade this generalized non extensive entropy has found many applications in plasma physics, astrophysics, fractals, turbulence, systems with long-range correlations and complex systems. In practice the new generalized thermostatistics reduces to the standard one when the interaction becomes short-ranged. Moreover, all the known theorems for standard statistics mechanics hold also in the new generalized form.

I got interested in the generalized non extensive statistical mechanics after a meeting at MIT in the fall of 1998 where Tsallis presented his new entropy. Then V. Latora, M. Baranger (MIT) and Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro) and I applied these concepts to understand the growth of the generalized entropy in the case of the logistic map at the edge-of-chaos, i.e. just at the critical point when the behavior of the logistic map changes from regular to chaotic. My fisrt paper on this subject was published in Physics Letters A (2000) and a second one is Chaos Solitons and Fractals. Others have been published in several journals, see below.

I got recently involved in the organization of several School/Conference on

"Non Extensive Thermodynamics and its applications", NEXT2001 , which was held in Sardinia (Italy) in may 2001 and in the second edition NEXT2003 and third edition NEXT05

  • For a recent review paper on the non extensive thermodynamics by C. Tsallis click here
  • For a short review on the non extensive thermodynamics available on the web site of the Santa Fe Institute for complex systems click here

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    Other related international conferences

  • Non extensive thermodynamics workshop at the Santa Fe Institute for complex systems, April 2002 click here for details
  • Workshop of the LOS ALAMOS Nat. Lab. on "Anomalous distributions", November 2002 click here for details
  • Workshop on Complexity, Metastability and Nonextensivity, Erice July 2004 click here for details
  • School and conference on Complex Systems and Nonextensive Statistical Mechanics, ICTP Trieste, Italy 31 July- 8 August 2006 click here for details.

    • Click here to see a recent video conference by Constantino Tsallis

      A few recent references:

    Web page with updated information on the Generalized statistics proposed by Tsallis

    A cover article by M. Buchanan published on the New Scientist issue of august 2005

    Special Issue of Europhysics News 36-6 (2005) dedicated to nonextensive statistics