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Generalized superstatistics of nonequilibrium Markovian systems

Author

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  • Lubashevsky, Ihor
  • Friedrich, Rudolf
  • Heuer, Andreas
  • Ushakov, Andrey

Abstract

The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff’s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes. The latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually. Then stationary probability as well as flux distributions are represented as some sums over the channels. The latter construction actually forms the superstatistical description, which, however, deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the Boltzmann type.

Suggested Citation

  • Lubashevsky, Ihor & Friedrich, Rudolf & Heuer, Andreas & Ushakov, Andrey, 2009. "Generalized superstatistics of nonequilibrium Markovian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4535-4550.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:21:p:4535-4550
    DOI: 10.1016/j.physa.2009.07.038
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    1. Ou, Congjie & El Kaabouchi, Aziz & Chen, Jincan & Le Méhauté, Alain & Wang, Qiuping A., 2009. "Stability of incomplete entropy and incomplete expectation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1813-1817.
    2. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    3. Luzzi, Roberto & R. Vasconcellos, Áurea & Galvão Ramos, J, 2004. "Nonequilibrium ensemble formalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 163-169.
    4. Beck, Christian, 2006. "Stretched exponentials from superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 96-101.
    5. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
    6. Hasegawa, Hideo, 2006. "Nonextensive aspects of small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 383-401.
    7. Chavanis, P.H. & Sire, C., 2005. "On the interpretations of Tsallis functional in connection with Vlasov–Poisson and related systems: Dynamics vs thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 419-446.
    8. Hanel, Rudolf & Thurner, Stefan, 2006. "On the derivation of power-law distributions within classical statistical mechanics far from the thermodynamic limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 162-166.
    9. Reynolds, A.M, 2004. "Superstatistical Lagrangian stochastic modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 298-308.
    10. Bashkirov, A.G, 2004. "On maximum entropy principle, superstatistics, power-law distribution and Renyi parameter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 153-162.
    11. Souza, Andre M.C. & Tsallis, Constantino, 2004. "Stability analysis of the entropies for superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 132-138.
    12. Briggs, Keith & Beck, Christian, 2007. "Modelling train delays with q-exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 498-504.
    13. Beck, C. & Cohen, E.G.D., 2004. "Superstatistical generalization of the work fluctuation theorem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 393-402.
    14. J. Perello & J. Masoliver & A. Kasprzak & R. Kutner, 2008. "A model for interevent times with long tails and multifractality in human communications: An application to financial trading," Papers 0805.1353, arXiv.org, revised Jul 2008.
    15. Beck, Christian, 2004. "Nonextensive scalar field theories and dark energy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 459-466.
    16. Chavanis, Pierre-Henri, 2006. "Coarse-grained distributions and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 177-212.
    17. Abul-Magd, A.Y., 2006. "Superstatistics in random matrix theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 41-54.
    18. Leon Chen, L. & Beck, Christian, 2008. "A superstatistical model of metastasis and cancer survival," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3162-3172.
    19. Beck, Christian, 2004. "Generalized statistical mechanics of cosmic rays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 173-181.
    20. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
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