L Yin and P Ao 2006 J. Phys. A: Math. Gen. 39 8593 doi:10.1088/0305-4470/39/27/003
L Yin1 and P Ao2
Show affiliationsThe 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.
89.75.Fb Structures and organization in complex systems
05.70.Ln Nonequilibrium and irreversible thermodynamics
05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
Issue 27 (7 July 2006)
Received 21 November 2005, in final form 27 April 2006
Published 21 June 2006
L Yin and P Ao 2006 J. Phys. A: Math. Gen. 39 8593
P Ao 2004 J. Phys. A: Math. Gen. 37 L25
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