Partially observable Szilárd engines

Abstract

Almost a century ago, Leo Szilárd replaced Maxwell’s ‘demon’ by machinery. The resulting information engine concept laid the foundation for studying the physical nature of information. Szilárd reduced the demon’s role to mapping an observable onto a work extraction protocol, thereby creating and utilizing a meta-stable memory. While Szilárd demonstrated that this map can be implemented mechanistically, it was not chosen automatically by the demon, or ‘observer’, but rather given a priori. This choice implements the demon’s intelligence. In Szilárd’s original setup, the choice is trivial, but we show here that nontrivial data representations emerge for generalized, partially observable Szilárd engines. Partial observability is pervasive in real world systems with limited sensor types and information acquisition bandwidths. Generalized information engines may run work extraction at a higher temperature than memory formation, which enables the combined treatment of heat- and information engines. To date, Szilárd’s (fully observable) information engine still serves as a canonical example. Implications of partial observability are under-explored, despite their ubiquitous nature. We provide here the first physical characterization of observer memories that result in minimal engine dissipation. We introduce a new canonical model, simple yet physically rich: a minor change to Szilárd’s engine—inserting the divider at an angle—results in partially observable engines. We demonstrate how the demon’s intelligence can be automated. For each angle and for each temperature ratio, an optimal memory is found algorithmically, enabling the engine to run with minimal dissipation. While naive coarse graining is sufficient for the special case of full observability, in general, minimally dissipative observers use probabilistic memories. We propose a simple model for an implementation of these memories, and construct a nontrivial physical codebook. We characterize the performance of engines with minimally dissipative memories, and compare their quality to that of engines using an optimized coarse graining of the observable.