Force Geometry and Irreversibility in Nonequilibrium Dynamics

TL;DR

This paper introduces force geometry as a key organizing principle in nonequilibrium thermodynamics, linking force orientation to irreversibility and dissipation patterns, and provides geometric control tools for experimental analysis.

Contribution

It formalizes the role of force alignment in entropy production, offering a geometric framework that explains dissipation heterogeneity and fluctuation-dissipation anticorrelation.

Findings

Entropy production depends on force orientation, vanishing under exact anti-alignment.

Perfect anti-alignment defines a thermodynamic stall with zero net transport.

Geometric control charts locate experimental points within force-space, aiding analysis.

Abstract

Recent experiments have revealed heterogeneous dissipation in optically trapped systems, often anticorrelated with local positional fluctuations, exposing a structural gap in the scalar stochastic thermodynamic description. While the conventional scalar framework successfully quantifies dissipation through currents and entropy production rates, it does not reveal the underlying vectorial force geometry that shapes spatial dissipation patterns. Here, we bridge this gap by identifying force geometry as an organizing principle for nonequilibrium thermodynamics and introducing force alignment as a geometric determinant of irreversibility. We show that entropy production depends not only on force magnitudes but also on the relative orientation between deterministic driving forces and entropic gradients, vanishing only under exact anti-alignment with matched magnitudes. We formalize this geometric alignment through a time-dependent force-correlation coefficient, quantifying the relative orientation between the forces. This yields an instantaneous geometric lower bound on entropy production that remains valid even when force magnitudes are matched. For overdamped dynamics, perfect anti-alignment defines a thermodynamic stall where net transport vanishes and the lower bound on entropy production is saturated. This force-level perspective provides a structural explanation for the experimentally observed fluctuation-dissipation anticorrelation and nonuniform dissipation. We construct geometric control charts for both constant dragging and sinusoidal driving protocols, explicitly locating experimental operating points within this force-space representation. Together, these results position force geometry as a unifying structural perspective on irreversibility, spanning active biological systems, microrheology, and naturally extending to underdamped dynamics.