Near equilibrium, entropy production governs relaxation. The system loses free energy, dissipation drives it downhill, and the time-asymmetric part of the dynamics — the part that distinguishes past from future — determines where the system goes. This is classical thermodynamics: irreversibility is the engine.
Maes and Netočný show that far from equilibrium, the engine changes. For systems relaxing toward a steady nonequilibrium state, it is the frenesy — the time-symmetric component of the dynamical action — that shapes macroscopic evolution. Not dissipation, not entropy production, but the total dynamical traffic: how much is happening, regardless of which direction it flows.
The frenesy measures activity. A system with high frenesy has frequent transitions, large fluctuations, intense microscopic motion — but the motion itself doesn't prefer past over future. It's the undirected hum of the system's dynamics. Near equilibrium, this hum is irrelevant because dissipation dominates. Far from equilibrium, dissipation is no longer the whole story. The frenesy acquires structure through a canonical Legendre decomposition, and that structure determines the relaxation pathway.
The result extends the GENERIC formalism — an established framework where equilibrium relaxation is a dissipative gradient flow superimposed on a Hamiltonian flow — to genuine nonequilibrium conditions. The extension hinges on local detailed balance, which identifies the thermodynamic forces, and the frenesy decomposition, which separates the time-symmetric dynamics into a Legendre pair that encodes both the cost and the structure of fluctuations.
The inversion is precise: near equilibrium, asymmetry (entropy production) drives the system. Far from equilibrium, symmetry (frenesy) shapes where the system goes. The arrow of time tells you less about the destination than the amount of traffic on the road.