Journal
PHYSICAL REVIEW E
Volume 106, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.106.054123
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Funding
- French Agence Nationale de la Recherche
- Idex Sorbonne Universite
- [Segal ANR-19-CE31-0017]
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This study examines the irreversible relaxation process of long-range interacting systems, describing it at both 1/N and 1/N2 orders. By deriving a collision operator suitable for long-range systems, the properties of the system and comparisons with theoretical simulations are explored.
Long-range interacting systems irreversibly relax as a result of their finite number of particles, N. At order 1/N, this process is described by the inhomogeneous Balescu-Lenard equation. Yet, this equation exactly vanishes in one-dimensional inhomogeneous systems with a monotonic frequency profile and sustaining only 1:1 resonances. In the limit where collective effects can be neglected, we derive a closed and explicit 1/N2 collision operator for such systems. We detail its properties, highlighting in particular how it satisfies an H theorem for Boltzmann entropy. We also compare its predictions with direct N-body simulations. Finally, we exhibit a generic class of long-range interaction potentials for which this 1/N2 collision operator exactly vanishes.
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