Fig. 3: Optimal sensing in the high-signal-correlation limit.

For perfectly correlated Gaussian signals, the nonequilibrium information gain is largest in the noiseless limit. We consider a sensor complex driven with signal H = (h, h) with \({P}_{H}\ =\ {e}^{-{h}^{2}/2}/\sqrt{2\pi }\). a The nonequilibrium gain as a function of sensor reliability β. The gain grows from zero at β = 1.7 and increases with β, suggesting that the enhancement results from the ability to distinguish additional signal features. b Optimal sensing strategy for varying noise levels. For β < 1 (shaded), the mutual information is maximised by an equilibrium system (t^* = 0) with infinitely strong coupling. The equilibrium strategy remains optimal for β < 1.7 with a coupling J^* (solid) that decreases with β and exhibits a sign change at β = 1.4. At bigger β, the optimal coupling in the equilibrium case (dashed) continues to decrease but equilibrium sensing becomes suboptimal. For β  > 1.7, the mutual information is maximised by a finite nonequilibrium drive (dot-dashed) and negative coupling.