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Updated: Sep 8, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Nonequilibrium master equation for interacting Brownian particles in a deep-well periodic potential
1Department of Physics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand.
Abstract:
Employing a creation and annihilation operator formulation, we derive an approximate many-body master equation describing discrete hopping from the more general continuous description of Brownian motion on a deep-well nonequilibrium periodic potential. The many-body master equation describes interactions of arbitrary strength and range arising from a "top-hat" two-body interaction potential. We show that this master equation reduces to the well-known asymmetric simple exclusion process and the zero range process in certain regimes. We also use the creation and annihilation operator formalism to derive results for the steady-state drift and the number fluctuations in special cases, including the unexplored limit of weak interparticle interactions.
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