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Lenard–Balescu correction
to mean-field theory
Mitia Duerinckx and Laure Saint-Raymond |
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Vol. 2 (2021), No. 1, 27–69
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Abstract |
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In the mean-field regime, the evolution of a gas of 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 . We show how one can derive rigorously this correction on intermediate timescales (of order for ) close to equilibrium. |
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Keywords
interacting particle system, mean-field limit, fluctuations
around thermal equilibrium, tagged particle,
thermalization, Lenard–Balescu kinetic equation, BBGKY
hierarchy, cumulant expansion, linearized Vlasov operator,
Markovian limit
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Mathematical Subject Classification 2010
Primary: 35Q70, 35Q82, 82D10
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Milestones
Received: 22 November 2019
Revised: 17 September 2020
Accepted: 19 October 2020
Published: 16 March 2021
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Authors |
| Mitia Duerinckx | |
| Université Paris-Saclay, CNRS Laboratoire de Mathématiques d’Orsay Orsay France |
Université Libre de Bruxelles Département de Mathématique Brussels Belgium |
| Laure Saint-Raymond | |
| Unité de mathématiques pures et
appliquées École Normale Supérieure de Lyon Lyon France |
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