Abstract
The fluctuation properties inherent in the variation principle of the Path Probability Method (PPM) devised by Kikuchi are extensively studied. First, as a prototype of a kinetic process the Becker-Doring nucleation theory is reformulated from the viewpoint of the PPM. Second, a general formulation of the PPM is reviewed with a spin flip model being taken as a model with interaction among particles. Third, the general formulation is applied to an inhomogeneous spin system in the point and the pair approximations. Not only the master equation for inhomogeneous magnetization but also the path integral representation is also obtained. Along a path called anticausal path the path integral representation is shown to give the creation of a free energy to be expected from the Cluster Variation Method (CVM) in equilibrium statistical mechanics. Concerning the magnetic susceptibility, the validity of the well known fluctuation dissipation theorem is confirmed. These facts show the consistency between the PPM and the CVM. Finally the master equation in the homogeneous system is numerically integrated in comparison with the Becker-Doring nucleation theory to study the relaxation from the metastable to stable states in the point and pair approximations. The nucleation rates are in good agreement with theoretical expectations.
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