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Coarse-grained distributions and superstatistics

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  • Chavanis, Pierre-Henri

Abstract

We show an interesting connection between non-standard (non-Boltzmannian) distribution functions arising in the theory of violent relaxation for collisionless stellar systems [D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136 (1967) 101.] and the notion of superstatistics recently introduced by [Beck and Cohen Physica A 322 (2003) 267]. The common link between these two theories is the emergence of coarse-grained distributions arising out of fine-grained distributions. The coarse-grained distribution functions are written as a superposition of Boltzmann factors weighted by a non-universal function. Even more general distributions can arise in case of incomplete violent relaxation (non-ergodicity). They are stable stationary solutions of the Vlasov equation. We also discuss analogies and differences between the statistical equilibrium state of a multi-components self-gravitating system and the metaequilibrium (or quasi-equilibrium) states of a collisionless stellar system. Finally, we stress the important distinction between entropies, generalized entropies, relative entropies and H-functions. We discuss applications of these ideas in two-dimensional turbulence and for other systems with long-range interactions.

Suggested Citation

  • Chavanis, Pierre-Henri, 2006. "Coarse-grained distributions and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 177-212.
    • Handle: RePEc:eee:phsmap:v:359:y:2006:i:c:p:177-212
    DOI: 10.1016/j.physa.2005.06.043
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    Cited by:

    1. Atenas, Boris & Curilef, Sergio, 2021. "A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    2. 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.
    3. 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.

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