Kinetic theory of collisionless relaxation for systems with long-range interactions
arXiv:2112.13664 · doi:10.1016/j.physa.2022.128089
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.
References in corpus (19)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
- A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
- Out-of-equilibrium tricritical point in a system with long-range interactions
- Lynden-Bell and Tsallis distributions for the HMF model
- Simpler Variational Problem for Statistical Equilibria of the 2D Euler Equation and Other Systems with Long Range Interactions
- Logotropic distributions
- Dynamical stability of collisionless stellar systems and barotropic stars: the nonlinear Antonov first law
- Landau equation for self-gravitating classical and quantum particles: Application to dark matter
- Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
- Kinetic theory of two dimensional point vortices from a BBGKY-like hierarchy
- Dynamics and thermodynamics of systems with long-range interactions: interpretation of the different functionals
- Predictive model of fermionic dark matter halos with a quantum core and an isothermal atmosphere
- Statistical mechanics of 2D turbulence with a prior vorticity distribution
- A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
- Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
- Thermodynamics of MHD flows with axial symmetry
- Topology of Collisionless Relaxation
- Statistical mechanics of violent relaxation in stellar systems
Cited by in corpus (9)
- 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- 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