Optimal encoding of information enables net work extraction from a partially observable Szilard engine*

In the classical Szilard engine, a Maxwell demon makes perfect measurements, and all stored information leads to work extraction.  However, a real system may produce ambiguous observations.  For example, a crooked divider in a Szilard engine could make it difficult to infer which side the particle is on.  Inspired by recent work of Daimer and Still (arXiv:2309.10476), we have experimentally realized optimally encoded measurements on a partially observable Szilard engine whose divider shape creates an ambiguous region in the middle.  The experiment uses feedback optical tweezers and a colloidal particle in water.   A deterministic 2-state memory, encoded as a double-well potential, leads to less work than a classical Szilard engine. We can offset the higher operational costs of memory devices by using the Szilard box at a higher temperature than the memory.   Adding a memory state (triple-well potential) to store the uncertain observations increases operational costs but also increases work extraction above a critical temperature for a given size of the ambiguous region.  Surprisingly, a probabilistic memory encoding can lead to greater work extraction than a deterministic encoding.