Variational characterization of free energy: Theory and algorithms

Please always quote using this URN: urn:nbn:de:0297-zib-65045
  • 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.

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Author:Carsten Hartmann, Lorenz Richter, Christof Schütte, Wei Zhang
Document Type:ZIB-Report
Tag:Donsker-Varadhan principle; Importance sampling; cross-entropy method; nonequilibrium molecular dynamics; stochastic approximation; thermodynamic free energy
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Axx Ergodic theory [See also 28Dxx] / 37A60 Dynamical systems in statistical mechanics [See also 82Cxx]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J60 Diffusion processes [See also 58J65]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
Date of first Publication:2017/10/06
Series (Serial Number):ZIB-Report (17-52)

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