Abstract
let p(x,t) be the probability density of a general diffusion process {x(t); (>_tST). A variational path-integral representation for the square root of p, and of \(\left( {p\sqrt p } \right),where{\text{ }}\overline p \) is the density of the invariant measure, is derived. This is accomplished by showing that these functions are optimal performances of stochastic controls problems, where the controlled equation evolves backward in time. This provides a rigorous counterpart of the formal Onsager-Machlup formulation of nonequilibrium thermodynamics. The research of this author was conducted at LADSEB-CNR, Padua, ITALY, with support provided by a CNR postgraduate fellowship.
The research of this author was conducted at LADSEB-CNR, Padua, ITALY, with support provided by a CNR postgraduate fellowship.
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© 1989 B. G. Teubner Stuttgart
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Pra, P.D., Pavon, M. (1989). A rigorous Onsager-Machlup formulation of nonequilibrium thermodynamics. In: Boffi, V., Neunzert, H. (eds) Proceedings of the Third German-Italian Symposium Applications of Mathematics in Industry and Technology. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96692-6_14
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DOI: https://doi.org/10.1007/978-3-322-96692-6_14
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