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Number of trials required to estimate a free-energy difference, using fluctuation relations

Yunger Halpern, Nicole and Jarzynski, Christopher (2016) Number of trials required to estimate a free-energy difference, using fluctuation relations. Physical Review E, 93 (5). Art. No. 052144. ISSN 1539-3755. doi:10.1103/PhysRevE.93.052144.

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The difference ΔF between free energies has applications in biology, chemistry, and pharmacology. The value of ΔF can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a ΔF estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly by Jarzynski [Phys. Rev. E 73, 046105 (2006)]. We enhance the approximation with the following information-theoretic strategies. We quantify “dominance” with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-∞ Rényi entropy. The bound can be estimated if one implements the “good practice” of bidirectionality, known to improve estimates of ΔF. Estimating ΔF from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.

Item Type:Article
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URLURL TypeDescription Paper
Yunger Halpern, Nicole0000-0001-8670-6212
Alternate Title:How many trials should you expect to perform to estimate a free-energy difference?
Additional Information:© 2016 American Physical Society. Received 25 January 2016; revised manuscript received 12 March 2016; published 26 May 2016. N.Y.H. is grateful for conversations with Tobias Fritz, Iman Marvian, Markus Müller, Brian Space, and Rob Spekkens. J.M.R. acknowledges helpful conversations with Michael Walter. This work was supported by a Virginia Gilloon Fellowship, an IQIM Fellowship, NSF Grant No. PHY-0803371, the Perimeter Institute for Theoretical Physics, the Swiss National Science Foundation (through the National Centre of Competence in Research Quantum Science and Technology and Grant No. 200020-135048), and the European Research Council (Grant No. 258932). The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center that receives support from the Gordon and Betty Moore Foundation. Research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. N.Y.H. is grateful to Renato Renner for hospitality at ETH Zürich during the development of this paper.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Virginia Gilloon FellowshipUNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Swiss National Science Foundation (SNSF)200020-135048
European Research Council (ERC)258932
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Issue or Number:5
Classification Code:PACS: 05.70.Ln, 05.40.-a, 05.70.Ce, 89.70.Cf
Record Number:CaltechAUTHORS:20160510-084438891
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66835
Deposited By: Tony Diaz
Deposited On:10 May 2016 19:42
Last Modified:11 Nov 2021 00:03

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