Heuristic derivation of continuum kinetic equations from microscopic dynamics
arXiv:cond-mat/0006217 · doi:10.1103/PhysRevE.63.016102
Abstract
We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field type, decoupled approximation of the master equation followed by the `naive' continuum limit. The Ising model and driven diffusive systems are used as illustrations. The equations derived are in agreement with other approaches, and consequences of the microscopic dependences of coarse-grained parameters compare favorably with exact or high-temperature expansions. The method is valuable when more systematic and rigorous approaches fail, and when microscopic inputs in the continuum theory are desirable.
7 pages, RevTeX, two-column, 4 PS figures included