Nondifferentiable potentials for nonequilibrium steady states
type: Item
instance of: scholarly article
title: Nondifferentiable potentials for nonequilibrium steady states
zbMATH Open document ID: 0669.58049
DOI: 10.1016/0378-4371(87)90151-8
author: H.-R. Jauslin
published in: Physica A
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://purl.umn.edu/4500
review text: In the weak noise limit of Fokker-Planck models, the stationary probability density can be expressed in the form \(P\sim \exp (-1/\epsilon \phi (x))\), where \(\epsilon\) measures the strength of the noise. We show firstly that, although in general \(\phi\) is not differentiable, it is regular enough to allow its use as a Lyapunov function for the underlying deterministic dynamical system. This justifies the interpretation of \(\phi\) as a generalized thermodynamic potential for systems away from equilibrium. Secondly, we show that the nondifferentiability of \(\phi\) does not presuppose any kind of irregular behavior in the underlying deterministic system, nor the presence of several stationary points. We construct a simple model with one single attractor and trivial deterministic dynamics, which has a nondifferentiable quasipotential \(\phi\). We relate the nondifferentiability to the existence of caustics and shock lines in the associated variational problem.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 80A99
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 4096453
zbMATH Keywords: weak noise limit of Fokker-Planck models
zbMATH Keywords: stationary probability density
zbMATH Keywords: generalized thermodynamic
MaRDI profile type: Publication
OpenAlex ID: W2089280070
cites work: Q3672830
cites work: On the weak-noise limit of Fokker-Planck models
cites work: Q5520199
cites work: Stability theory by Liapunov's direct method
cites work: Q5842044
cites work: Q4743352
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description: scientific article; zbMATH DE number 4096453