Heuristic derivation of continuum kinetic equations from microscopic dynamics

Details Heuristic derivation of continuum kinetic equations from microscopic dynamics Heuristic derivation of continuum kinetic equations from microscopic dynamics

2000-06-14

arxiv.org/abs/cond-mat/0006217v1

Physical Review E, Vol.63, 016102 (2001).

Physics

Condensed Matter

Statistical Mechanics

7 pages, RevTeX, two-column, 4 PS figures included

Scientific paper

10.1103/PhysRevE.63.016102

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.

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