Lenard–Balescu correction to mean-field theory

• DOI: 10.2140/pmp.2021.2.27
• Publication Date: 2021-03-17T04:25:11Z
• Authors: Mitia Duerinckx; Laure Saint-Raymond
• Keywords: Mean field theory; Operator (biology); Vlasov Equation; Landau damping

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