Residual dynamics determine dissipation in strongly coupled linear Langevin systems

Interactions shape the properties of many physical and biological nonequilibrium systems, but whether collective operation raises or lowers entropy production remains difficult to predict. Here, we show that strong coupling suppresses irreversible circulation associated with the directly coupled degrees of freedom. In identical two-dimensional systems, this suppression is monotonic for nonzero coupling modes and guarantees a monotonic decrease of the entropy production rate (EPR), with the corresponding probability currents vanishing in the strong-coupling limit. In higher dimensions, suppressing the circulation associated with the coupled degrees of freedom does not generally eliminate all irreversible circulation, since the remaining degrees of freedom can still sustain nonequilibrium currents. The EPR of these residual dynamics sets the strong-coupling limit, providing a criterion for whether a given choice of coupled variables leads to lower dissipation than the uncoupled system. The approach to this limit depends on how the finite-coupling current correction aligns with the residual current. Further, we show that convergence to residual dynamics in the strong-coupling limit also applies to coupled non-identical systems. Finally, we demonstrate the predicted EPR reduction in nonlinear models of vertebrate hair-cell bundles and bacterial chemotaxis.