Optimal work extraction and the minimum description length principle

Abstract

We discuss work extraction from classical information engines (e.g., Szilárd) with N-particles, q partitions, and initial arbitrary non-equilibrium states. In particular, we focus on their optimal behaviour, which includes the measurement of a set of quantities Φ with a feedback protocol that extracts the maximal average amount of work. We show that the optimal non-equilibrium state to which the engine should be driven before the measurement is given by the normalised maximum-likelihood probability distribution of a statistical model that admits Φ as sufficient statistics. Furthermore, we show that the minimax universal code redundancy associated to this model, provides an upper bound to the work that the demon can extract on average from the cycle, in units of kBT. We also find that, in the limit of N large, the maximum average extracted work cannot exceed H[Φ]/2, i.e. one half times the Shannon entropy of the measurement. Our results establish a connection between optimal work extraction in stochastic thermodynamics and optimal universal data compression, providing design principles for optimal information engines. In particular, they suggest that: (i) optimal coding is thermodynamically efficient, and (ii) it is essential to drive the system into a critical state in order to achieve optimal performance.