Phase transition in the Jarzynski estimator of free energy differences
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...
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| Formato: | Artigo |
| Idioma: | en_US |
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American Physical Society
2012
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| Acesso em linha: | http://hdl.handle.net/1721.1/71629 |
| _version_ | 1826217800784412672 |
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| author | Suarez Gonzalez, Alberto Silbey, Robert J. Oppenheim, Irwin |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Suarez Gonzalez, Alberto Silbey, Robert J. Oppenheim, Irwin |
| author_sort | Suarez Gonzalez, Alberto |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T17:09:21Z |
| format | Article |
| id | mit-1721.1/71629 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:09:21Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/716292022-09-30T00:03:27Z Phase transition in the Jarzynski estimator of free energy differences Suarez Gonzalez, Alberto Silbey, Robert J. Oppenheim, Irwin Massachusetts Institute of Technology. Department of Chemistry Oppenheim, Irwin Suarez Gonzalez, Alberto Silbey, Robert J. Oppenheim, Irwin 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. DGI (Spain) (TIN2010-21575- C02-02) 2012-07-16T18:32:12Z 2012-07-16T18:32:12Z 2012-05 2012-02 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/71629 ©2012 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevE.85.051108 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Suarez Gonzalez, Alberto Silbey, Robert J. Oppenheim, Irwin Phase transition in the Jarzynski estimator of free energy differences |
| title | Phase transition in the Jarzynski estimator of free energy differences |
| title_full | Phase transition in the Jarzynski estimator of free energy differences |
| title_fullStr | Phase transition in the Jarzynski estimator of free energy differences |
| title_full_unstemmed | Phase transition in the Jarzynski estimator of free energy differences |
| title_short | Phase transition in the Jarzynski estimator of free energy differences |
| title_sort | phase transition in the jarzynski estimator of free energy differences |
| url | http://hdl.handle.net/1721.1/71629 |
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