Escape problem for irreversible systems

Journal Article · Sun Aug 01 04:00:00 EDT 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.48.931· OSTI ID:6027065

Maier, R S ^[1]; Stein, D L ^[2]

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1. Department of Mathematics, University of Arizona, Tuscon, Arizona 85721 (United States)
2. Department of Physics, University of Arizona, Tuscon, Arizona 85721 (United States)

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 [ital focusing] along the escape path.

• DOE Contract Number: FG03-93ER25155
• OSTI ID: 6027065
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 48:2; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DETAILED BALANCE PRINCIPLE
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
EQUATIONS
EXCITED STATES
FOCUSING
INVARIANCE PRINCIPLES
IRREVERSIBLE PROCESSES
METASTABLE STATES
NOISE
STOCHASTIC PROCESSES
T INVARIANCE
TIMING PROPERTIES