Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 37, Issue 3, Pages L25-L30Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/37/3/L01
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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.
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