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

Abstract

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, 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.

References in corpus (9)

• Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique
• Molecular dynamics of open systems: construction of a mean-field particle reservoir
• Adaptive Resolution Molecular Dynamics Technique: Down to the Essential
• Probing Spatial Locality in Ionic Liquids with the Grand Canonical Adaptive Resolution Molecular Dynamics Technique
• Grand Canonical Adaptive Resolution Simulation for Molecules with Electrons: A Theoretical Framework based on Physical Consistency
• Towards Open Boundary Molecular Dynamics Simulation of Ionic Liquids
• Nanoscale domains in ionic liquids: A statistical mechanics definition for molecular dynamics studies
• Simulation of many-electron systems that exchange matter with the environment
• Adaptive Boundaries in Multiscale Simulations

Cited by in corpus (8)

• Open Systems out of Equilibrium: Theory and Simulation
• A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations
• Chemical diffusion master equation: formulations of reaction--diffusion processes on the molecular level
• Thermodynamic relations at the coupling boundary in adaptive resolution simulations for open systems
• Simulation of a particle domain in a continuum/fluctuating hydrodynamics reservoir
• Nonequilibrium induced by reservoirs: Physico-mathematical models and numerical tests
• Open quantum systems and the grand canonical ensemble
• Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems