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

H. Hasegawa | Zendy

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

Author(s) -

H. Hasegawa

Publication year - 1976

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.56.44

Subject(s) - physics , gaussian , mathematical physics , variational principle , scalar (mathematics) , quadratic equation , operator (biology) , boundary value problem , order (exchange) , quantum mechanics , mathematics , biochemistry , chemistry , geometry , repressor , transcription factor , gene , finance , economics

where al{p, V(S)} and P"{p,X(S)} are the dissipation functional expressed as a quadratic form of the velocity field V(S) and the force field X(p), respectively, averaged over the distribution p. Here, the p 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.

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