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

Pierre-Henri Chavanis

Physica A: Statistical Mechanics and its Applications, 2022, vol. 606, issue C

Abstract: 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.

Keywords: Collisionless relaxation; Lynden-Bell statistical theory; Vlasov equation; Kinetic theory; Generalized entropy; Dynamical stability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122006756

DOI: 10.1016/j.physa.2022.128089

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