Geometric Dissipation Constraints in Stochastic Reaction Dynamics: A Variational Observable for Hidden Kinetic Structure in Energy Landscapes

Abstract

We propose a geometric framework for characterizing hidden kinetic constraints in stochastic reaction dynamics. While free-energy barriers and entropy production provide global descriptors of thermodynamic behavior, they are largely insensitive to local geometric structure in configuration space that governs pathway selection. Starting from overdamped Langevin dynamics formulated as a gradient flow in Wasserstein space, we derive a variational functional whose leading-order asymptotic structure defines a local dissipation-geometry coupling observable. This quantity combines force-drift alignment with phase-space contraction induced by the divergence of the drift field, yielding a scalar field that reflects second-order geometric features of the underlying energy landscape. We demonstrate that this observable distinguishes kinetically distinct reaction channels that are degenerate under conventional free-energy analysis, as shown through numerical experiments on benchmark systems including the Muller-Brown potential, corrugated periodic landscapes, and the conformational transitions of Alanine Dipeptide. These experiments demonstrate robust separation of pathways and are consistent with a quadratic scaling behavior in the high-frequency homogenization regime. Our results suggest that stochastic reaction dynamics contain an additional geometric layer of kinetic control in molecular motion not captured by standard thermodynamic or reaction-coordinate descriptions.