Work extraction with feedback control using limited resources

Many physical, biological, and even social systems are faced with the problem of how to efficiently harvest free energy from an environment that can have many possible states, yet only have a limited number of harvesting protocols to choose among. We investigate this scenario by extending earlier work on using feedback control to extract work from nonequilibrium systems. Specifically, in contrast to that previous work on the thermodynamics of feedback control, we analyze the combined and separate effects of noisy measurements, memory limitations, and limitations on the number of possible work extraction protocols. Our analysis provides a general recipe to construct repertoires of allowed harvesting protocols that minimize the expected thermodynamic losses during free energy harvesting, i.e., that minimize expected entropy production. In particular, our results highlight that the benefits of feedback control over uninformed (random) actions extend beyond just the associated information gain, often by many orders of magnitude. Our results also uncover the effects of limitations on the number of possible harvesting protocols when there is uncertainty about the distribution over states of the environment.