Weak convergence to equilibrium of statistical ensembles in integrable Hamiltonian systems
This article explores the long-time behavior of the bounded orbits associated with an ensemble of initial conditions in a nondegenerate integrable Hamiltonian system. Such systems are inherently nonlinear and subject to highly regular phase space filamentation that can drive the ensemble of orbits toward a stationary state. Describing the statistical ensemble by a probability density on a neighborhood of a family of invariant tori, it is proved that the probability density describing the ensemble at time t converges weakly to an invariant density as t → ∞. More generally, we provide sufficient conditions for convergence to equilibrium of a multiphase system in action-angle form. These ideas are applied to an illustrative exactly soluble example. Finally, this work is relevant for understanding the statistical mechanics of integrable and near-integrable Hamiltonian systems
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1581067
- Alternate ID(s):
- OSTI ID: 1511777
- Journal Information:
- Journal of Mathematical Physics, Vol. 60, Issue 5; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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