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Entropy 2017, 19(11), 626; https://doi.org/10.3390/e19110626

Variational Characterization of Free Energy: Theory and Algorithms

1
Institut für Mathematik, Brandenburgische Technische Universität Cottbus-Senftenberg, D-03046 Cottbus, Germany
2
Institut für Mathematik, Freie Universität Berlin, D-14195 Berlin, Germany
3
Zuse Institute Berlin, D-14195 Berlin, Germany
*
Author to whom correspondence should be addressed.
Received: 25 September 2017 / Revised: 7 November 2017 / Accepted: 15 November 2017 / Published: 20 November 2017
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
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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. View Full-Text
Keywords: importance sampling; Donsker–Varadhan principle; thermodynamic free energy; nonequilibrium molecular dynamics; stochastic approximation; cross-entropy method importance sampling; Donsker–Varadhan principle; thermodynamic free energy; nonequilibrium molecular dynamics; stochastic approximation; cross-entropy method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Hartmann, C.; Richter, L.; Schütte, C.; Zhang, W. Variational Characterization of Free Energy: Theory and Algorithms. Entropy 2017, 19, 626.

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