Liouville-type equations for the n-particle distribution functions of an open system

In this work, we derive a mathematical model for an open system that exchanges particles and momentum with a reservoir from their joint Hamiltonian dynamics. The complexity of this many-particle problem is addressed by introducing a countable set of n-particle phase space distribution functions just...

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Bibliographic Details
Published in:Journal of mathematical physics 2020-08, Vol.61 (8)
Main Authors: Delle Site, Luigi, Klein, Rupert
Format: Article
Language:English
Subjects:
Computer simulation
Distribution functions
Liouville equations
Mathematical models
Momentum
Open systems
Physics
Reservoirs
Statistical analysis
Subsystems
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Summary:In this work, we derive a mathematical model for an open system that exchanges particles and momentum with a reservoir from their joint Hamiltonian dynamics. The complexity of this many-particle problem is addressed by introducing a countable set of n-particle phase space distribution functions just for the open subsystem, while accounting for the reservoir only in terms of statistical expectations. From the Liouville equation for the full system, we derive a set of coupled Liouville-type equations for the n-particle distributions by marginalization with respect to reservoir states. The resulting equation hierarchy describes the external momentum forcing of the open system by the reservoir across its boundaries, and it covers the effects of particle exchanges, which induce probability transfers between the n- and (n + 1)-particle distributions. Similarities and differences with the Bergmann–Lebowitz model of open systems [P. G. Bergmann and J. L. Lebowitz, Phys. Rev. 99, 578–587 (1955)] are discussed in the context of the implementation of these guiding principles in a computational scheme for molecular simulations.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0008262