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Canonical equilibrium distribution derived from Helmholtz potential


  • Oikonomou, Thomas
  • Baris Bagci, G.
  • Tirnakli, Ugur


Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

Suggested Citation

  • Oikonomou, Thomas & Baris Bagci, G. & Tirnakli, Ugur, 2012. "Canonical equilibrium distribution derived from Helmholtz potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6386-6389.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6386-6389 DOI: 10.1016/j.physa.2012.07.072

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    References listed on IDEAS

    1. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283,
    2. Liu, Chuang & Zhou, Wei-Xing & Yuan, Wei-Kang, 2010. "Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2675-2681.
    3. Yang, Yue & Wang, Jianbo & Yang, Huijie & Mang, Jingshi, 2009. "Visibility graph approach to exchange rate series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4431-4437.
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