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Mechanism for asymmetric bias in demonstrations of the NPI and fluctuation theorem

Petersen, Charlotte; Evans, Denis; Williams, Stephen

Description

We consider two different methods of calculating the relevant average for the non-equilibrium partition identity (NPI), i.e. (Formula presented.), which result in two different values. At best only one of these will accurately correspond to what is observed. In order to better understand the two outcomes we carry out a detailed error analysis. This analysis is difficult due to the importance of extremely rare events in forming the average, resulting in the necessity to go beyond linear...[Show more]

dc.contributor.authorPetersen, Charlotte
dc.contributor.authorEvans, Denis
dc.contributor.authorWilliams, Stephen
dc.date.accessioned2016-02-24T22:41:06Z
dc.identifier.issn0892-7022
dc.identifier.urihttp://hdl.handle.net/1885/98562
dc.description.abstractWe consider two different methods of calculating the relevant average for the non-equilibrium partition identity (NPI), i.e. (Formula presented.), which result in two different values. At best only one of these will accurately correspond to what is observed. In order to better understand the two outcomes we carry out a detailed error analysis. This analysis is difficult due to the importance of extremely rare events in forming the average, resulting in the necessity to go beyond linear approximations for the error estimates. We begin by analysing the error in the fluctuation relation, and build upon this to estimate the errors in the NPI average. At short durations the full ensemble average always gives the observed average (i.e. the NPI holds). However, at very long durations, given a fixed amount of sampling, the observed average is predicted by treating the probability distribution as a Dirac-delta function. At intermediate times, neither corresponds to the observed average. This has profound implications for non-equilibrium work relations, as first introduced by Jarzynski.
dc.publisherTaylor & Francis Group
dc.sourceMolecular Simulation
dc.titleMechanism for asymmetric bias in demonstrations of the NPI and fluctuation theorem
dc.typeJournal article
local.description.notesImported from ARIES
dc.date.issued2015
local.identifier.absfor030700 - THEORETICAL AND COMPUTATIONAL CHEMISTRY
local.identifier.absfor030704 - Statistical Mechanics in Chemistry
local.identifier.ariespublicationU3488905xPUB6045
local.type.statusPublished Version
local.contributor.affiliationPetersen, Charlotte, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationEvans, Denis, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationWilliams, Stephen, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage1
local.bibliographicCitation.lastpage12
local.identifier.doi10.1080/08927022.2015.1068940
dc.date.updated2016-02-24T10:09:25Z
local.identifier.scopusID2-s2.0-84941711850
CollectionsANU Research Publications

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