The Geometry of Most Probable Trajectories in Noise-Driven Dynamical Systems

TL;DR

This paper develops a geometric minimum action method to identify the most probable transition paths in noise-driven dynamical systems, especially those violating detailed balance, with applications demonstrated in a quadratic shear flow.

Contribution

It introduces a heuristic geometric approach for calculating most-probable trajectories in non-equilibrium systems with stochastic vorticity effects.

Findings

Identifies bifurcating transition pathways in shear flow

Highlights the role of stochastic vorticity tensor

Provides a method applicable to systems violating detailed balance

Abstract

This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed balance, and the role of the stochastic vorticity tensor is emphasized. The general method is explored through a detailed study of a two-dimensional quadratic shear flow which exhibits bifurcating most-probable transition pathways.