Title: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. Almost a hundred years later, Szilard's information engine still serves as a canonical example, despite significant growth of the field in the last decade. The role the demon plays can be reduced to mapping observable data to a meta-stable memory which is then utilized to extract work. While Szilard showed that the map can be implemented mechanistically, the map 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. They provide the basis for understanding the physical nature of information processing. Here, we propose a simple model that nonetheless displays physical richness. A minor change to Silard's engine - inserting the divider at an angle - results in a family of partially observable Szilard engines. Their analysis illustrates how the demon's intelligence can be automated. At fixed angle, there is an optimal memory for each value of $T'/T$, enabling maximal engine efficiency. Those memories are probabilistic. They are computed by an algorithm derived from minimizing dissipation. We compare their quality to that of naive, deterministic coarse graining of the observable, and connect the method of finding optimal data representations to the computation of a rate-distortion function.