Existence and construction of dynamical potential in nonequilibrium processes without detailed balance
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The existence of a dynamical potential with both local and global meanings in general nonequilibrium processes has been controversial. Following an earlier heuristic argument in a letter by one of us, in the present paper we show rigorously its existence for a generic class of situations in physical and biological sciences. The local dynamical meaning of this potential function is demonstrated via a special stochastic differential equation and its global steady-state meaning via a novel and explicit form of the Fokker–Planck equation. We also give a procedure to obtain the special stochastic differential equation for any given Fokker–Planck equation. No detailed balance condition is required in our demonstration. For the first time we obtain here a formula to describe the noise-induced shift in drift force compared to the steady-state distribution, a phenomenon extensively observed in numerical studies.
Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics
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In Computer Networks and Communications
In Statistical and Nonlinear Physics
Citations in the corpus
- Relation of a New Interpretation of Stochastic Differential Equations to Ito Process (2011, background): “Related issues have been considered along the line [2, 5, 14, 15, 28].”
- A Complete Recipe for Stochastic Gradient MCMC (2015, background): “(4) can be further transformed into a more compact form [19, 16]: We can verify that p ( z | S ) is invariant under Eq.”