Partially Observable Szilard Engines

Abstract

Leo Szilard pointed out that Maxwell's demon can be replaced by machinery, thereby laying the foundation for understanding the physical nature of information. Szilard's information engine still serves as a canonical example after almost a hundred years, despite recent significant growth of the area. The role the demon plays can be reduced to mapping observable data to a meta-stable memory, which is utilized to extract work. While Szilard showed that the map can be implemented mechanistically, it was chosen a priori. The choice of how to construct a meaningful memory constitutes the demon's intelligence. Recently, it was shown that this can be automated as well. To that end, generalized, partially observable information engines were introduced, providing a basis for understanding the physical nature of information processing. Partial observability is ubiquitous in real world systems which have limited sensor types and information acquisition bandwidths. Generalized information engines can run work extraction at a different temperature, T' > T, from the memory forming process. This enables the combined treatment of heat engines and information engines. We study the physical characteristics of intelligent observers by introducing a canonical model that displays physical richness, despite its simplicity. A minor change to Szilard's engine - inserting the divider at an angle - results in a family of partially observable Szilard engines. Their analysis shows how the demon's intelligence can be automated. For each angle, and for each value of T'/T, an optimal memory can be found, enabling the engine to run with minimal dissipation. Those optimal memories are probabilistic maps, computed algorithmically. We discuss how they can be implemented with a simple physical system, characterize their performance, and compare their quality to that of naive, deterministic quantizations of the observable.

arXiv comment33 pages, fixed typos and rephrased small parts, also combined some figures. Results and conclusions remain unchanged. New Journal of Physics (2022)

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