On the accurate estimation of free energies using the jarzynski equality

The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is e...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Arrar, M., Boubeta, F.M., Szretter, M.E., Sued, M., Boechi, L., Rodriguez, D.
Formato:	JOUR
Materias:	free energy Jarzynski maximum-likelihood steered molecular dynamics Free energy Gaussian distribution Maximum likelihood Maximum likelihood estimation Molecular dynamics Sampling Accurate estimation Bennett acceptance ratio Fluctuation dissipation Maximum likelihood estimators (MLE) Nonequilibrium transition Second-order approximation Steered molecular dynamics Parameter estimation
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_01928651_v40_n4_p688_Arrar
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_01928651_v40_n4_p688_Arrar
record_format	dspace
spelling	todo:paper_01928651_v40_n4_p688_Arrar2023-10-03T15:09:11Z On the accurate estimation of free energies using the jarzynski equality Arrar, M. Boubeta, F.M. Szretter, M.E. Sued, M. Boechi, L. Rodriguez, D. free energy Jarzynski maximum-likelihood steered molecular dynamics Free energy Gaussian distribution Maximum likelihood Maximum likelihood estimation Molecular dynamics Sampling Accurate estimation Bennett acceptance ratio Fluctuation dissipation Jarzynski Maximum likelihood estimators (MLE) Nonequilibrium transition Second-order approximation Steered molecular dynamics Parameter estimation The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, (Formula presented.). Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator (Formula presented.). Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy (Formula presented.) considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to (Formula presented.). We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional (Formula presented.) to the Bennett acceptance ratio ((Formula presented.)) estimator. We show that, for Gaussian unidirectional work distributions, (Formula presented.) is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that (Formula presented.) and (Formula presented.) perform better than (Formula presented.) and (Formula presented.), for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01928651_v40_n4_p688_Arrar
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	free energy Jarzynski maximum-likelihood steered molecular dynamics Free energy Gaussian distribution Maximum likelihood Maximum likelihood estimation Molecular dynamics Sampling Accurate estimation Bennett acceptance ratio Fluctuation dissipation Jarzynski Maximum likelihood estimators (MLE) Nonequilibrium transition Second-order approximation Steered molecular dynamics Parameter estimation
spellingShingle	free energy Jarzynski maximum-likelihood steered molecular dynamics Free energy Gaussian distribution Maximum likelihood Maximum likelihood estimation Molecular dynamics Sampling Accurate estimation Bennett acceptance ratio Fluctuation dissipation Jarzynski Maximum likelihood estimators (MLE) Nonequilibrium transition Second-order approximation Steered molecular dynamics Parameter estimation Arrar, M. Boubeta, F.M. Szretter, M.E. Sued, M. Boechi, L. Rodriguez, D. On the accurate estimation of free energies using the jarzynski equality
topic_facet	free energy Jarzynski maximum-likelihood steered molecular dynamics Free energy Gaussian distribution Maximum likelihood Maximum likelihood estimation Molecular dynamics Sampling Accurate estimation Bennett acceptance ratio Fluctuation dissipation Jarzynski Maximum likelihood estimators (MLE) Nonequilibrium transition Second-order approximation Steered molecular dynamics Parameter estimation
description	The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, (Formula presented.). Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator (Formula presented.). Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy (Formula presented.) considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to (Formula presented.). We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional (Formula presented.) to the Bennett acceptance ratio ((Formula presented.)) estimator. We show that, for Gaussian unidirectional work distributions, (Formula presented.) is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that (Formula presented.) and (Formula presented.) perform better than (Formula presented.) and (Formula presented.), for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.
format	JOUR
author	Arrar, M. Boubeta, F.M. Szretter, M.E. Sued, M. Boechi, L. Rodriguez, D.
author_facet	Arrar, M. Boubeta, F.M. Szretter, M.E. Sued, M. Boechi, L. Rodriguez, D.
author_sort	Arrar, M.
title	On the accurate estimation of free energies using the jarzynski equality
title_short	On the accurate estimation of free energies using the jarzynski equality
title_full	On the accurate estimation of free energies using the jarzynski equality
title_fullStr	On the accurate estimation of free energies using the jarzynski equality
title_full_unstemmed	On the accurate estimation of free energies using the jarzynski equality
title_sort	on the accurate estimation of free energies using the jarzynski equality
url	http://hdl.handle.net/20.500.12110/paper_01928651_v40_n4_p688_Arrar
work_keys_str_mv	AT arrarm ontheaccurateestimationoffreeenergiesusingthejarzynskiequality AT boubetafm ontheaccurateestimationoffreeenergiesusingthejarzynskiequality AT szretterme ontheaccurateestimationoffreeenergiesusingthejarzynskiequality AT suedm ontheaccurateestimationoffreeenergiesusingthejarzynskiequality AT boechil ontheaccurateestimationoffreeenergiesusingthejarzynskiequality AT rodriguezd ontheaccurateestimationoffreeenergiesusingthejarzynskiequality
_version_	1782024066208628736

On the accurate estimation of free energies using the jarzynski equality

Ejemplares similares