Entropy production reveals hidden dynamical constraints rather than stochastic disorder

Abstract: Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in which local noise, geometry, and forces are held fixed while global constraints are varied. Trajectories are generated for particles evolving toward a central attractor, and entropy production is quantified using both a continuum probability-current estimator and coarse-grained Markov transition statistics across multiple spatial and temporal resolutions. Across systematic sweeps of timestep size, domain extent, and boundary topology, entropy production is governed primarily by constraint-induced probability flow rather than local stochastic variability. Periodic domains that permit sustained circulation yield substantially higher entropy production than reflecting domains despite identical local stochastic structure, with the magnitude of the separation depending on domain extent. In contrast, coarse-grained estimates decrease as temporal resolution increases and rise with finer spatial binning, demonstrating that discrete estimates depend strongly on observation scale and may fail to resolve topology-induced irreversible structure. Ergo, entropy production is not a direct measure of environmental roughness or randomness. Instead, it quantifies how strongly system dynamics are driven away from reversibility by global constraints, geometry, and the space of allowed trajectories. Interpreted in this way, entropy production maps function as diagnostics of organized probability flow and provide a principled method for detecting hidden dynamical constraints from trajectory data alone.