Escape problem for irreversible systems

Robert S Maier, D. L. Stein

Research output: Contribution to journalArticle

127 Citations (Scopus)

Abstract

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.

Original languageEnglish (US)
Pages (from-to)931-938
Number of pages8
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume48
Issue number2
DOIs
StatePublished - 1993

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escape
Detailed Balance
Asymptotic Behavior
Path
Metastable States
Nonlinear Dynamical Systems
Systems Engineering
Probable
Chemistry
Biology
Continuous Time
Resolve
Simplify
Ordinary differential equation
Partial differential equation
Physics
biology
Computing
systems engineering
metastable state

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Escape problem for irreversible systems. / Maier, Robert S; Stein, D. L.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 48, No. 2, 1993, p. 931-938.

Research output: Contribution to journalArticle

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