Observable and hidden singular features of large fluctuations in nonequilibrium systems

TL;DR

This paper investigates the topological structure of large fluctuations in nonequilibrium systems, revealing observable singularities and differences from quantum extremal paths, with implications for understanding rare events.

Contribution

It introduces a topological framework for analyzing large fluctuations, highlighting observable singularities and the unique behavior of optimal paths in nonequilibrium systems.

Findings

Optimal paths do not encounter caustics unlike in quantum mechanics.

Observable singularities differ from caustics and can originate at saddle points.

The study provides insights into the global structure of fluctuation patterns.

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.