Fig. 2. Optimal sensing for correlated signals.

Nonequilibrium sensing is optimal in the low-noise, high-correlation limit for correlated Gaussian signals. a We assume that the signal directly influences both sensors with varying correlation, Eq. (10). b The optimal coupling J^* as a function of sensor reliability β and the signal redundancy, i.e., the mutual information between the input signals I(h₁; h₂). The optimal coupling diverges J^* → ∞ at small β (region I, left of the dashed curve) and decreases with larger β. Between the dashed and solid curves (region II), the mutual information I(S; H) is maximised by equilibrium sensors with a finite J^* that changes from cooperative (red) to anticooperative (blue) at the dotted line. Nonequilibrium sensing is the optimal strategy for signals with relatively high redundancy in the low-noise limit (region III, above the solid curve).