Phase transition in the Jarzynski estimator of free energy differences
Entidad
UAM. Departamento de Ingeniería InformáticaEditor
American Physical SocietyFecha de edición
2012-05-07Cita
10.1103/PhysRevE.85.051108
Physical Review E 85.5 (2012): 051108
ISSN
1539-3755 (print); 1550-2376 (online)DOI
10.1103/PhysRevE.85.051108Financiado por
The authors thank Eric Zimanyi for insightful discussions. A.S. acknowledges partial financial support from the Spanish Dirección General de Investigación, project TIN2010-21575- C02-02.Versión del editor
http://dx.doi.org/10.1103/PhysRevE.85.051108Materias
Informática; TelecomunicacionesDerechos
© 2012 American Physical SocietyResumen
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.
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Google Scholar:Suárez González, Alberto
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Silbey, Robert
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Oppenheim, Irwin
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