Variational Characterization of Free Energy: Theory and Algorithms

Abstract

The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.

Keywords

• importance sampling
• Donsker–Varadhan principle
• thermodynamic free energy
• nonequilibrium molecular dynamics
• stochastic approximation
• cross-entropy method