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

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 [P.H. Chavanis, Physica A {\bf 332}, 89 (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.

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• Collisionless relaxation of a Lynden-Bell plasma
• Galaxy rotation curves and universal scaling relations: comparison between phenomenological and fermionic dark matter profiles
• Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence
• Modelling the Track of the GD-1 Stellar Stream Inside a Host with a Fermionic Dark Matter Core-Halo Distribution
• Dimensional measures of generalized entropy
• Using Kernel-Based Statistical Distance to Study the Dynamics of Charged Particle Beams in Particle-Based Simulation Codes
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect
• Thermodynamics of self-gravitating fermions as a robust theory for dark matter halos: Stability analysis applied to the Milky Way
• A Collision Operator for Field-Mediated Interactions in General Relativistic Kinetic Theory
• Predicting the Final Stationary State of Sheared 2D Euler Fluids