Linear embedding of free energy minimization

Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to attain. Such properties include the preservation of convexity, lower bounds on free energy, and applicability to systems without subsystem structure. We satisfy all of these properties by embedding free energy minimization into a linear program over energy-resolved expectation values. Numerical results on small systems are encouraging, but a lack of size consistency necessitates further development for large systems.