Observable partitioning under uncertainty in information engines with physically implemented observer memories*

Generalized partially observable information engines were introduced recently to study the physical foundations of information processing and decision making under uncertainty [PRL 124(5)050601, 2020]. In [NJP (24)073031, 2022], we analyzed the physical characteristics of observer memories that maximize average engine work output of a canonical example. Optimal memories cannot be achieved by coarse graining, but rather are nontrivial probabilistic (``soft") partitions of the observable. While our model was simple, the resulting physical rules for constructing the memories were complex.

Coarse graining is ubiquitous in physics, but soft partitions are not. Intuition quickly fails. Here, we present an even simpler model to build physical intuition, namely a parameterized version of the example given in [PRL 124(5)050601, 2020]. We find that the physical process governing optimal observer memories is indeed easy to understand. We also compare optimal memories to coarse graining and soft partition approximations, obtained via parametric optimization, which is computationally less costly. Soft partition approximations give better performance.

It is worthwhile thinking about whether this broadening of the scope of possible ways to partition the observable might have useful consequences for other physical models that rely on coarse graining.