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Article Dans Une Revue Physica A Année : 2022

Kinetic theory of collisionless relaxation for systems with long-range interactions

Résumé

We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation obtained from the quasilinear theory of the Vlasov equation and the relaxation equation obtained from a maximum entropy production principle. We propose a method to close the infinite hierarchy of kinetic equations for the phase level moments and obtain a kinetic equation for the coarse-grained distribution function in the form of a generalized Landau, Lenard–Balescu or Kramers equation associated with a generalized form of entropy (Chavanis, 2004). This allows us to go beyond the two-level case associated with a Fermi–Dirac-type entropy. We discuss the numerous analogies with two-dimensional turbulence. We also mention possible applications of the present formalism to fermionic and bosonic dark matter halos.

Dates et versions

hal-03519710 , version 1 (10-01-2022)

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Citer

Pierre-Henri Chavanis. Kinetic theory of collisionless relaxation for systems with long-range interactions. Physica A, 2022, 606, pp.128089. ⟨10.1016/j.physa.2022.128089⟩. ⟨hal-03519710⟩
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