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The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2161–2175 | Cite as

Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics

  • C. Tsallis
  • L.J.L. Cirto
Review
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications

Abstract

We briefly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermo-dynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs (BG) statistical mechanics is sufficient but not necessary. Indeed, the N →∞ limit of statistical mechanics is expected to be consistent with thermodynamics. For systems whose elements are generically independent or quasi-independent in the sense of the theory of probabilities, it is well known that the BG theory (based on the additive BG entropy) does satisfy this expectation. However, in complete analogy, other thermostatistical theories (e.g., q-statistics), based on nonadditive entropic functionals, also satisfy the very same expectation. We illustrate this standpoint with systems whose elements are strongly correlated in a specific manner, such that they escape the BG realm.

Keywords

Entropy Black Hole Statistical Mechanic European Physical Journal Special Topic Classical Thermodynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex SystemsRio de Janeiro-RJBrazil
  2. 2.Santa Fe InstituteSanta FeUSA

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