Evaluation of Thermodynamic Averages in a Phase Space with Overlapping Subdomains

We demonstrate a simple methodology for accurately and efficiently evaluating the ensemble average of thermodynamic observables across a phase space divided into arbitrary, potentially overlapping, subdomains defined, for example, via corresponding collective variables or descriptors. By dividing the phase space in this manner, the challenging task of sampling the complete phase space is rigorously transformed into relatively easier sampling over subdomains, each of which can be sampled independently and without regard to their mutual overlap. Accurate thermal averages of observables over the complete phase space are then obtained by sampling over these subdomains and properly reweighting them based on their degree of mutual overlap at each point in phase space. To demonstrate the efficacy of our approach, we examine applications to simple Lennard-Jones clusters and subsequently to ion clusters in aqueous solution, where the various cluster connectivities and morphologies provide a natural division of phase space. More generally, we anticipate that our approach holds promise for a wide range of applications, from nucleation free energy surfaces to the thermodynamics of protein conformational changes, providing a natural complement to traditional enhanced sampling methods.