On the Construction of a Time-Reversed Markoff Process

概要

論文の詳細を見る
For a given Markoff process characterized by a set of transition probability densities these exits another process with time reversed (the retrodictive vs predictive process in the theory of measurements) such that any one of them multiplied by a single-event density may by symmetric with respect to an interchange of the events expressed as space-time variables, yielding a joint probability density. It is shown how this time-reversed process can be constructed by means of the generating operator of the associated evolution equation, and the basic properties with explicit applications to master equations and Fokker-Planck equations. Onsager's with explicit applications to master equations and Fokker-Planck equations. Onsager's microscopic reversibility is reformulated on this basis. Possible symmetries concerning time-correlation functions under the Markoffian law is summarized in comparion with the Kubo formula. In the application to Fokker-Planck equations, the Onsager-Machlup most probable paths are extended to general type of diffusion processes, and it is shown that the present method corresponds to a gauge transformation in dynamics of a charged particle which leaves its paths invariant.
理論物理学刊行会の論文
1976-01-25