Phase Transition in a noisy information engine is avoided by using Bayesian inference*

Information engines use observations of thermal fluctuations as "fuel" to extract work or produce directed motion. Inspired by the classic thought experiment of Maxwell, they have clarified our understanding of the interplay between information and the second law of thermodynamics. We investigated the role of uncertainties in the measurements used to power the information engine. Surprisingly, there is a critical level of measurement noise, above which a pure information engine — one where no external work is needed — is no longer possible. The reason can be traced back to a bias in the naive use of measurements by the information engine. The bias has two sources: time delays and a subtle error arising whenever decisions are based on rare events and depend on noisy measurements. We then used a more sophisticated Bayesian way of incorporating the entire history of past measurements (predictive Kalman filter). By removing both biases, the Bayesian approach allows the information engine to function at all levels of measurement noise. In the regime where thermal fluctuations are comparable to the measurement noise, the performance gain over a naive approach is significant, pointing to practical information engines that operate with minimal information-processing costs.