Lenard-Balescu correction to mean-field theory

Abstract

In the mean-field regime, the evolution of a gas of $N$ interacting particles is governed in first approximation by a Vlasov type equation with a self-induced force field. This equation is conservative and describes return to equilibrium only in the very weak sense of Landau damping. However, the first correction to this approximation is given by the Lenard-Balescu operator, which dissipates entropy on the very long timescale $O(N)$. In this paper, we show how one can derive rigorously this correction on intermediate timescales (of order $O(N^r)$ for $r<1$), close to equilibrium.

arXiv comment41 pages

References in corpus (6)

• On the Dynamics of Large Particle Systems in the Mean Field Limit
• From particle systems to the Landau equation: a consistency result
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
• On the Linearized Balescu-Lenard Equation
• The two-particle correlation function for systems with long-range interactions

Cited by in corpus (7)

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• Dynamical large deviations for plasmas below the Debye length and the Landau equation
• Well-posedness of the Lenard-Balescu equation with smooth interactions
• Non-perturbative solutions of hierarchies of evolution equations for colliding particles
• Dynamics of point-vortex type systems near thermal equilibrium: relaxation or not?