Potential in stochastic differential equations: novel construction
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- 6 January 2004
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 37 (3) , L25-L30
- https://doi.org/10.1088/0305-4470/37/3/l01
Abstract
There is a whole range of emergent phenomena in a complex network such as robustness, adaptiveness, multiple-equilibrium, hysteresis, oscillation and feedback. Those non-equilibrium behaviours can often be described by a set of stochastic differential equations. One persistent important question is the existence of a potential function. Here we demonstrate that a dynamical structure built into stochastic differential equation allows us to construct such a global optimization potential function. We present an explicit construction procedure to obtain the potential and relevant quantities. In the procedure no reference to the Fokker–Planck equation is needed. The availability of the potential suggests that powerful statistical mechanics tools can be used in nonequilibrium situations.All Related Versions
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