The bleary-eyed Maxwell demon: a mutual information-fueled colloidal engine

The Maxwell-meets-Shannon problem of a demon who observes a thermal system through a noisy information channel is omnipresent in non-equilibrium physics, and in particular in living systems where signaling and perception are often prone to noise. Yet, the direct measurement of the information-energy interplay of these demons with bleary vision has so far been elusive for continuous systems. Here, by directly controlling and gauging the capacity of the demon’s detection channel, we extract the full mutual information-work performance curve for a cyclic colloidal engine operating in nonequilibrium steady-state and study the efficiency fluctuations. We find that the most efficient engines, are far from perfect and utilize only about 0.5-1 bits of positional information per cycle. At this noise level of maximal average efficiency, the distribution of efficiency switches from bimodal to unimodal, and the stochastic efficiency often exceeds the bound set by the generalized second law. We identify a line of anomalous, noise-driven equilibrium states that defines a refrigerator-to-heater transition. Crossing this line, the thermodynamic measurables and their fluctuations switch their behavior, and the generalized integral fluctuation theorem passes through unity.