DOI: 10.1073/pnas.0406405101. Experimental test of Hatano and Sasa's nonequilibrium steady-state equality

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

10.1073/pnas.0406405101

Crossref journal-article

Proceedings of the National Academy of Sciences

Proceedings of the National Academy of Sciences (341)

Abstract

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, –ln〈 e – Y 〉 = 0. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that –ln〈 e – Y 〉 ≈ 0 for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.

Bibliography

Trepagnier, E. H., Jarzynski, C., Ritort, F., Crooks, G. E., Bustamante, C. J., & Liphardt, J. (2004). Experimental test of Hatano and Sasaâs nonequilibrium steady-state equality. Proceedings of the National Academy of Sciences, 101(42), 15038â15041.

Authors 6

E. H. Trepagnier (first)
C. Jarzynski (additional)
F. Ritort (additional)
G. E. Crooks (additional)
C. J. Bustamante (additional)
J. Liphardt (additional)

References 29 Referenced 210

10.1109/3.992554
10.1073/pnas.152007599
Goldbeter A. (1997) in Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour (Cambridge Univ. Press London). (10.1017/CBO9780511608193)
10.1038/24409
Keizer J. (1987) in Statistical Thermodynamics of Nonequilibrium Processes (Springer Berlin). (10.1007/978-1-4612-1054-2)
10.1088/0034-4885/51/8/002
Eu B. C. (1998) in Nonequilibrium Statistical Mechanics (Kluwer Academic Dordrecht The Netherlands). (10.1007/978-94-017-2438-8)
10.1143/PTPS.130.29
Finn C. B. P. (1993) in Thermal Physics (Chapman and Hall London) 2nd Ed..
10.1063/1.448273
10.1103/PhysRevLett.86.3463
Chandler D. (1987) in Introduction to Modern Statistical Mechanics (Oxford Univ. Press New York) Sect. 5.5.
10.1103/PhysRevLett.74.1504
10.1103/PhysRevLett.85.78
10.1103/PhysRevLett.89.050601
10.1073/pnas.071034098
10.1126/science.1071152
Mazonka O. & Jarzynski C. (Dec. 7 1999) arXiv.org:cond-mat 9912121.
10.1016/S0076-6879(03)61009-8
10.1073/pnas.1635159100
10.1016/S0009-2614(01)01397-5
10.1103/PhysRevLett.89.180602
10.1063/1.1590311
10.1073/pnas.172525099
10.1103/PhysRevLett.78.2690
10.1103/PhysRevE.56.5018
10.1023/A:1023208217925
10.1088/0034-4885/66/11/R03
Efron B. & Tibshirani R. J. (1993) in An Introduction to the Bootstrap (CRC New York). (10.1007/978-1-4899-4541-9)

Dates

Type	When
Created	20 years, 10 months ago (Oct. 6, 2004, 8:24 p.m.)
Deposited	3 years, 4 months ago (April 12, 2022, 9:25 a.m.)
Indexed	1 month ago (July 28, 2025, 5:40 p.m.)
Issued	20 years, 10 months ago (Oct. 6, 2004)
Published	20 years, 10 months ago (Oct. 6, 2004)
Published Online	20 years, 10 months ago (Oct. 6, 2004)
Published Print	20 years, 10 months ago (Oct. 19, 2004)

Funders 0

None

BibTeX

@article{Trepagnier_2004, title={Experimental test of Hatano and Sasa’s nonequilibrium steady-state equality}, volume={101}, ISSN={1091-6490}, url={http://dx.doi.org/10.1073/pnas.0406405101}, DOI={10.1073/pnas.0406405101}, number={42}, journal={Proceedings of the National Academy of Sciences}, publisher={Proceedings of the National Academy of Sciences}, author={Trepagnier, E. H. and Jarzynski, C. and Ritort, F. and Crooks, G. E. and Bustamante, C. J. and Liphardt, J.}, year={2004}, month=oct, pages={15038–15041} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        28
      ]
    ],
    "date-time": "2025-07-28T21:40:00Z",
    "timestamp": 1753738800682
  },
  "reference-count": 29,
  "publisher": "Proceedings of the National Academy of Sciences",
  "issue": "42",
  "content-domain": {
    "domain": [
      "www.pnas.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2004,
        10,
        19
      ]
    ]
  },
  "abstract": "<jats:p>\n            Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi [Oono, Y. &amp; Paniconi, M. (1998)\n            <jats:italic>Prog. Theor. Phys. Suppl.</jats:italic>\n            130, 29\u201344] proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium steady states and transitions between such states. In 2001, Hatano and Sasa [Hatano, T. &amp; Sasa, S. (2001)\n            <jats:italic>Phys. Rev. Lett.</jats:italic>\n            86, 3463\u20133466] derived a testable prediction of this theory. Specifically, they were able to show that the exponential average of\n            <jats:italic>Y</jats:italic>\n            , a quantity similar to a dissipated work, should be equal to zero for arbitrary transitions between nonequilibrium steady states, \u2013ln\u2329\n            <jats:italic>e</jats:italic>\n            <jats:sup>\n              \u2013\n              <jats:italic>Y</jats:italic>\n            </jats:sup>\n            \u232a = 0. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that \u2013ln\u2329\n            <jats:italic>e</jats:italic>\n            <jats:sup>\n              \u2013\n              <jats:italic>Y</jats:italic>\n            </jats:sup>\n            \u232a \u2248 0 for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.\n          </jats:p>",
  "DOI": "10.1073/pnas.0406405101",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        10,
        7
      ]
    ],
    "date-time": "2004-10-07T00:24:01Z",
    "timestamp": 1097108641000
  },
  "page": "15038-15041",
  "update-policy": "http://dx.doi.org/10.1073/pnas.cm10313",
  "source": "Crossref",
  "is-referenced-by-count": 210,
  "title": "Experimental test of Hatano and Sasa's nonequilibrium steady-state equality",
  "prefix": "10.1073",
  "volume": "101",
  "author": [
    {
      "given": "E. H.",
      "family": "Trepagnier",
      "sequence": "first",
      "affiliation": [
        {
          "name": "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 F\u00edsica Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"
        }
      ]
    },
    {
      "given": "C.",
      "family": "Jarzynski",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "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 F\u00edsica Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"
        }
      ]
    },
    {
      "given": "F.",
      "family": "Ritort",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "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 F\u00edsica Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"
        }
      ]
    },
    {
      "given": "G. E.",
      "family": "Crooks",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "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 F\u00edsica Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"
        }
      ]
    },
    {
      "given": "C. J.",
      "family": "Bustamante",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "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 F\u00edsica Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"
        }
      ]
    },
    {
      "given": "J.",
      "family": "Liphardt",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "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 F\u00edsica Fonamental, Universitat de Barcelona, Barcelona 08028, Spain; and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"
        }
      ]
    }
  ],
  "member": "341",
  "published-online": {
    "date-parts": [
      [
        2004,
        10,
        6
      ]
    ]
  },
  "reference": [
    {
      "key": "e_1_3_2_1_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/3.992554"
    },
    {
      "key": "e_1_3_2_2_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1073/pnas.152007599"
    },
    {
      "key": "e_1_3_2_3_2",
      "doi-asserted-by": "crossref",
      "unstructured": "Goldbeter A. (1997) in Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour (Cambridge Univ. Press London).",
      "DOI": "10.1017/CBO9780511608193"
    },
    {
      "key": "e_1_3_2_4_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/24409"
    },
    {
      "key": "e_1_3_2_5_2",
      "doi-asserted-by": "crossref",
      "unstructured": "Keizer J. (1987) in Statistical Thermodynamics of Nonequilibrium Processes (Springer Berlin).",
      "DOI": "10.1007/978-1-4612-1054-2"
    },
    {
      "key": "e_1_3_2_6_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1088/0034-4885/51/8/002"
    },
    {
      "key": "e_1_3_2_7_2",
      "doi-asserted-by": "crossref",
      "unstructured": "Eu B. C. (1998) in Nonequilibrium Statistical Mechanics (Kluwer Academic Dordrecht The Netherlands).",
      "DOI": "10.1007/978-94-017-2438-8"
    },
    {
      "key": "e_1_3_2_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1143/PTPS.130.29"
    },
    {
      "key": "e_1_3_2_9_2",
      "unstructured": "Finn C. B. P. (1993) in Thermal Physics (Chapman and Hall London) 2nd Ed.."
    },
    {
      "key": "e_1_3_2_10_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.448273"
    },
    {
      "key": "e_1_3_2_11_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.86.3463"
    },
    {
      "key": "e_1_3_2_12_2",
      "unstructured": "Chandler D. (1987) in Introduction to Modern Statistical Mechanics (Oxford Univ. Press New York) Sect. 5.5."
    },
    {
      "key": "e_1_3_2_13_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.74.1504"
    },
    {
      "key": "e_1_3_2_14_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.85.78"
    },
    {
      "key": "e_1_3_2_15_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.89.050601"
    },
    {
      "key": "e_1_3_2_16_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1073/pnas.071034098"
    },
    {
      "key": "e_1_3_2_17_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1071152"
    },
    {
      "key": "e_1_3_2_18_2",
      "unstructured": "Mazonka O. & Jarzynski C. (Dec. 7 1999) arXiv.org:cond-mat 9912121."
    },
    {
      "key": "e_1_3_2_19_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/S0076-6879(03)61009-8"
    },
    {
      "key": "e_1_3_2_20_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1073/pnas.1635159100"
    },
    {
      "key": "e_1_3_2_21_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/S0009-2614(01)01397-5"
    },
    {
      "key": "e_1_3_2_22_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.89.180602"
    },
    {
      "key": "e_1_3_2_23_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1590311"
    },
    {
      "key": "e_1_3_2_24_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1073/pnas.172525099"
    },
    {
      "key": "e_1_3_2_25_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.78.2690"
    },
    {
      "key": "e_1_3_2_26_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevE.56.5018"
    },
    {
      "key": "e_1_3_2_27_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1023/A:1023208217925"
    },
    {
      "key": "e_1_3_2_28_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1088/0034-4885/66/11/R03"
    },
    {
      "key": "e_1_3_2_29_2",
      "doi-asserted-by": "crossref",
      "unstructured": "Efron B. & Tibshirani R. J. (1993) in An Introduction to the Bootstrap (CRC New York).",
      "DOI": "10.1007/978-1-4899-4541-9"
    }
  ],
  "container-title": "Proceedings of the National Academy of Sciences",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pnas.org/doi/pdf/10.1073/pnas.0406405101",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2022,
        4,
        12
      ]
    ],
    "date-time": "2022-04-12T13:25:26Z",
    "timestamp": 1649769926000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pnas.org/doi/full/10.1073/pnas.0406405101"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2004,
        10,
        6
      ]
    ]
  },
  "references-count": 29,
  "journal-issue": {
    "issue": "42",
    "published-print": {
      "date-parts": [
        [
          2004,
          10,
          19
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1073/pnas.0406405101"
  ],
  "URL": "http://dx.doi.org/10.1073/pnas.0406405101",
  "relation": {},
  "ISSN": [
    "0027-8424",
    "1091-6490"
  ],
  "subject": [],
  "container-title-short": "Proc. Natl. Acad. Sci. U.S.A.",
  "published": {
    "date-parts": [
      [
        2004,
        10,
        6
      ]
    ]
  },
  "assertion": [
    {
      "value": "2004-10-06",
      "order": 2,
      "name": "published",
      "label": "Published",
      "group": {
        "name": "publication_history",
        "label": "Publication History"
      }
    }
  ]
}