Generalized-master-equation analysis of a ferromagnet model

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Abstract
The method of generalized master equations (GME) is used to investigate the nonequilibrium properties of a mean-field ferromagnet model in interaction with a bath. The Zwanzig projection techniques, modified to include coarse graining, provide the tool for obtaining various GME's at various levels of description. Results obtained by Goldstein and Scully and by Wang are shown to follow from the GME's in the long-time limit and an undesirable assumption, which was necessary in an earlier analysis, is eliminated. Explicit expressions are calculated for several quantities relevant to the evolution of the probabilities and their moments. Short-time results, characteristic of the underlying microscopic equations and inaccessible to the traditional analysis, are shown to follow from the GME, with a specific illustration for a simple two-spin system. This work thus complements the earlier analysis of Goldstein and Scully.