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

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Petersen, Charlotte; Evans, Denis; Williams, Stephen
Description
We consider two different methods of calculating the relevant average for the nonequilibrium 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.author  Petersen, Charlotte  

dc.contributor.author  Evans, Denis  
dc.contributor.author  Williams, Stephen  
dc.date.accessioned  20160224T22:41:06Z  
dc.identifier.issn  08927022  
dc.identifier.uri  http://hdl.handle.net/1885/98562  
dc.description.abstract  We consider two different methods of calculating the relevant average for the nonequilibrium 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 Diracdelta function. At intermediate times, neither corresponds to the observed average. This has profound implications for nonequilibrium work relations, as first introduced by Jarzynski.  
dc.publisher  Taylor & Francis Group  
dc.source  Molecular Simulation  
dc.title  Mechanism for asymmetric bias in demonstrations of the NPI and fluctuation theorem  
dc.type  Journal article  
local.description.notes  Imported from ARIES  
dc.date.issued  2015  
local.identifier.absfor  030700  THEORETICAL AND COMPUTATIONAL CHEMISTRY  
local.identifier.absfor  030704  Statistical Mechanics in Chemistry  
local.identifier.ariespublication  U3488905xPUB6045  
local.type.status  Published Version  
local.contributor.affiliation  Petersen, Charlotte, College of Physical and Mathematical Sciences, ANU  
local.contributor.affiliation  Evans, Denis, College of Physical and Mathematical Sciences, ANU  
local.contributor.affiliation  Williams, Stephen, College of Physical and Mathematical Sciences, ANU  
local.description.embargo  20371231  
local.bibliographicCitation.startpage  1  
local.bibliographicCitation.lastpage  12  
local.identifier.doi  10.1080/08927022.2015.1068940  
dc.date.updated  20160224T10:09:25Z  
local.identifier.scopusID  2s2.084941711850  
Collections  ANU Research Publications 
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