Observable and hidden singular features of large fluctuations in nonequilibrium systems

1994/10/17 by M. I. Dykman, Mark I. Dykman, Mark M. Millonas +2 · 3 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Nonlinear Dynamics and Pattern Formation #cond-mat #stochastic dynamics and bifurcation

paper · pdf · doi:10.1016/0375-9601(94)90426-x

10 pages, 3 ps figures by request, LaTeX Article Format (In press, Phys. Lett. A)

arxiv created 1994/10/17 · openalex publication_date 1994/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to extremal paths in quantum mechanics, the optimal paths do \it not encounter caustics. We show how this occurs, and what, instead of caustics, are the experimentally observable singularities of the pattern. We reveal the possibility for a caustic and a switching line to start at a saddle point, and discuss the consequences.

Citations

• Techniques and Applications of Path Integration
• Waves and Thom's theorem

Cited by

• Self-Consistent Microscopic Theory of Fluctuation-Induced Transport
• Large rare fluctuations in systems with delayed dissipation
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit