Thermal mechanics: A quantum mechanical analogue of nonequilibrium statistical thermodynamics

✍ Scribed by J.-C. Zambrini; K. Yasue

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 858 KB
• Volume: 125
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(80)90123-2

✦ Synopsis

A formal but not conventional equivalence between stochastic processes in nonequilibrium statistical thermodynamics and Schriidinger dynamics in quantum mechanics is shown. It is found, for each stochastic process described by a stochastic differential equation of Ito type, there exists a Schrodinger-like dynamics in which the absolute square of a wavefunction gives us the same probability distribution as the original stochastic process. In utilizing this equivalence between them, that is, rewriting the stochastic differential equation by an equivalent Schriidinger equation, it is possible to obtain the notion of de terministic limit of the stochastic process as a semi-classical limit of the "Schradinger" equation. The deterministic limit thus obtained improves the conventional deterministic approximation in the sense of Onsager-Machlup.

The present approach is valid for a general class of stochastic equations where local drifts and diffusion coefficients depend on the position. Two concrete examples are given. It should be noticed that the approach in the present form has nothing to do with the conventional one where only a formal similarity between the Fokker-Planck equation and the Schriidinger equation is considered.