Phase transition in the Jarzynski estimator of free energy differences
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Suarez-2012-Phase transition in the Jarzynski estimator of.pdf
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Author(s)
Suarez Gonzalez, Alberto
Silbey, Robert J.
Oppenheim, Irwin
Date Issued
May 2012
Journal
Physical Review E
Publisher
American Physical Society
Citation
©2012 American Physical Society
Version
Final published version
Abstract
The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems the directionality of time is poorly defined and the configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled. As the system size increases the arrow of time becomes better defined. The dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available. Asymptotically, only typical work values are measured. The Jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work, which is the result that is expected from standard macroscopic thermodynamics. In the proper scaling limit, this regime change has been recently described in terms of a phase transition in variants of the random energy model. In this paper this correspondence is further demonstrated in two examples of physical interest: the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.85.051108
