Onsager principle for nonlinear mechanical systems modeled by stochastic dissipative equations - Battezzati, M. (Archives of Mechanics, 2012)
A classical mechanical system subjected to frictional forces is considered in the limit of large frictional coefficient. Random white noise is also introduced in conformity to the fluctuation-dissipation theorem. The velocity is split into a deterministic component plus a random stochastic component consequently, the evolution operator (generator) for the probability density in configuration space is evaluated recalling previous work by the same author, by stochastically averaging the flux of particles. The averages depend upon the history of the system, but memory may be eliminated by suitably defining the drift, in the limit of large time. The fundamental solution of the diffusion equation is recast into the form of a Feynman path integral, and subsequently transformed into an Onsager–Machlup path integral, whose regressive stationary solutions satisfy the minimum entropy production principle. It is focused upon the role played by the appropriate definition of drift velocity adopted in this approach, allowing for interpretation of the Onsager–Machlup potential