| Popis: |
Nonequilibrium steady states (NESS) give rise to nontrivial cyclic probability fluxes that breach detailed balance (DB), and thus it is not clear how to define a potential analog to the equilibrium case. In this thesis we argue that possibly there is a formal way to define such a NESS potential for systems describable by a Fokker-Planck equation. DB in NESS can be restored [1] by mapping the phase space into a parameterized family of non- intersecting cycles containing the invariant manifolds of the corresponding deterministic, dynamical system. Transition rates between neighboring cycles are obtained from the microscopic dynamics, i.e., from the drift and diffusive currents. Since fluxes between cycles obey DB, we can integrate over the set of cycles. We present some evidence that this gives us a nonequilibrium potential which reaches minimum solely for NESS. The main goal of this thesis is to put forward a tentative theory for deriving a generalized potential function whose extrema identify the NESS. We will present results of a first numerical test based on two well-known dynamical systems: the van-der-Pol oscillator and the Brusselator. Our results, although not conclusive, are encouraging. |
