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PHYSICS
Experimental test of Hatano and Sasa's nonequilibrium steady-state equality

E. H. Trepagnier ^*, , C. Jarzynski , F. Ritort , G. E. Crooks ^¶, C. J. Bustamante ^{*, , ||, **}, and J. Liphardt ^*, , ||, 

^*Biophysics Graduate Group and Departments of ^||Physics, ^**Molecular and Cell Biology, and ^¶Plant and Microbial Biology, University of California, Berkeley, CA 94720; Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545; Departament de Física Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Contributed by C. J. Bustamante, September 3, 2004

Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi [Oono, Y. & Paniconi, M. (1998) Prog. Theor. Phys. Suppl. 130, 29–44] proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium steady states and transitions between such states. In 2001, Hatano and Sasa [Hatano, T. & Sasa, S. (2001) Phys. Rev. Lett. 86, 3463–3466] derived a testable prediction of this theory. Specifically, they were able to show that the exponential average of Y, a quantity similar to a dissipated work, should be equal to zero for arbitrary transitions between nonequilibrium steady states, –lne^–Y = 0. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that –lne^–Y 0 for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.

To whom correspondence should be addressed. E-mail: liphardt{at}physics.berkeley.edu.

© 2004 by The National Academy of Sciences of the USA

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