Variational Principle for Non-Equilibrium States and the Onsager-Machlup Formula

概要

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We consider diffusion processes with a general second-order differential operator of the elliptic type to extend the Onsager-Machlup theory of Gaussioan Markoff processes, and establish the two-gate joint probability formula [numerical formula] where φ{ρ,V(S)} and Ψ{ρ,X(S)} and the dissipation functional expressed as a quadratic form of the velocity field V(S) and the force field X(ρ), respectively, averaged over the distribution ρ. Here, the ρ and S are the two conjugate scalar fields (functions of state variables x as well as of time t) in the variational formulation for the pair of diffusion equations analogous to those for the Schrodinger equations, whose explicit forms are given in terms of a solution of the diffusion equations under a specified boundary condition.
理論物理学刊行会の論文
1976-07-25