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Drifts versus forces: The Ehrenfest theorem for Markovian diffusions. (English) Zbl 0959.82514
Summary: Following Stratonovich, we make a general analysis of the external force manifestations in the dynamics of Markov diffusion processes. The transformation connecting transition densities of the process with the respective (unique) Feynman-Kac kernels induces the local field of accelerations, which equals the gradient of the Feynman-Kac potential and enters the straightforward analog of the Ehrenfest theorem. The latter encompasses not only Nelson’s or Zambrini’s diffusions but also the familiar non-equilibrium statistical physics processes, like the standard Brownian motion in the external force field (Smoluchowski diffusions).
MSC:
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
81P20 Stochastic mechanics (including stochastic electrodynamics)
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