Skewed Thermodynamic Geometry and Optimal Free Energy Estimation

Accurate and precise measurements of free energy differences are crucial to the determination of stable phases of matter and the design of novel pharmaceutical ligands for targeted protein binding. We extend the thermodynamic-geometry framework to higher-order moments of energy dissipation, accounting for time-reversal asymmetry, which allows us to design protocols (dynamic variations of control parameters) that maximize the accuracy and precision of free energy estimators. In a model system, we find that these designed protocols can improve the precision by a factor of 3-4, and accuracy by over a factor of 10.