Gap to the Optimal n-State Engine in Asymptotic Work Extraction

Determine how close the information engines learned via thermodynamic machine learning—specifically, maximum-work training constrained to n predictive states—are to the optimal n-state information engines for the same input processes, measured by the asymptotic average work rate on test data.

Background

The paper derives an exact expression for the asymptotic work rate of an information engine and demonstrates training and testing performance under memory constraints. In discussing empirical results (e.g., Fig. 4) the authors note that larger memories can approach thermodynamic limits on long training sequences, but they explicitly acknowledge uncertainty about how close these learned engines are to the best possible n-state engines.

This uncertainty concerns the optimality gap between the learned maximum-work model (within the class of n-state predictive models) and the true optimum n-state engine with respect to asymptotic work extraction on data from the true process.