Stochastic thermodynamics of Gaussian information engines

Stochastic thermodynamics is an emerging field of research that has received considerable attention in the past two decades. Among its most visible applications is to understand the connections between information and thermodynamics. Recent theoretical advances in this field have established that the second law of thermodynamics, suitably modified to account for information, sets the limits of information-to-energy conversion; however, these limits are generally derived for systems that are ideal and assume that all of the system's energy can be extracted. Real systems on the other hand face constraints that may prevent them, both in principle as well as in practice, from achieving the predicted theoretical limits. Prompted by recent advances in experimental capabilities which allow for a high degree of control of mesoscopic systems, we explore the limits of information-to-work conversion in a simple "textbook example" colloid-based information engine that is implementable in the lab. We use this engine to explore the limits of information-to-work conversion when the engine is restricted to operate in a mode where long-term energy storage is prioritized. We find that restricting the engine to this mode of operation severely limits its ability to convert information to work compared to when the engine is optimized for raw energy extraction, without regards for whether the energy is stored or not. Nevertheless, in certain cases, it is possible to design the feedback control to have a work input which guarantees the engine stores energy at the highest achievable rate. We therefore find that information engines sometimes convert information to work most effectively when there is a mixture of external work input and information processing. Additionally, real engines face the conundrum of measurement noise. This complicates the feedback control and introduces biases in the estimates of the relevant thermodynamic quantities. To eliminate this bias, we use either a filter or we introduce feedback delays. Both strategies successfully eliminate the bias in the estimates; however, we find that using the filter has an additional benefit in that it allows us to compute a trajectory-level estimate of the information-processing costs. These results inform our theoretical understanding of the limits of real systems that convert information to work and provides the first measure of the information-processing costs for continuous variables.