[Comparaison des relations de travail loin de l'équilibre]
De récentes prédictions théoriques et mesures expérimentales ont démontré que les différences d'énergie libre d'équilibre peuvent s'obtenir à partir de moyennes exponentielles des valeurs du travail de non-équilibre. Ces résultats sont semblables en structure mais non équivalents à des prédictions dérivées il y a près de trente ans par Bochkov et Kuzovlev, et qui sont aussi formulées en termes de moyennes exponentielles mais qui n'impliquent pas de différences d'énergie libre. Dans le présent article, la relation entre ces deux ensembles de résultats est élucidée et ensuite illustrée par un modèle soluble de niveau élémentaire. L'analyse sert aussi à clarifier les interprétations physiques des différentes définitions du travail qui ont été utilisées dans le contexte des systèmes thermodynamiques maintenus hors d'équilibre.
Recent theoretical predictions and experimental measurements have demonstrated that equilibrium free energy differences can be obtained from exponential averages of nonequilibrium work values. These results are similar in structure, but not equivalent, to predictions derived nearly three decades ago by Bochkov and Kuzovlev, which are also formulated in terms of exponential averages but do not involve free energy differences. In the present article the relationship between these two sets of results is elucidated, then illustrated with an undergraduate-level solvable model. The analysis also serves to clarify the physical interpretation of different definitions of work that have been used in the context of thermodynamic systems driven away from equilibrium.
Publié le :
Mot clés : Systèmes non-équilibres, Relations de travail
@article{CRPHYS_2007__8_5-6_495_0,
author = {Christopher Jarzynski},
title = {Comparison of far-from-equilibrium work relations},
journal = {Comptes Rendus. Physique},
pages = {495--506},
publisher = {Elsevier},
volume = {8},
number = {5-6},
year = {2007},
doi = {10.1016/j.crhy.2007.04.010},
language = {en},
}
Christopher Jarzynski. Comparison of far-from-equilibrium work relations. Comptes Rendus. Physique, Volume 8 (2007) no. 5-6, pp. 495-506. doi : 10.1016/j.crhy.2007.04.010. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.04.010/
[1] Phys. Today, 58 (2005), p. 43
[2] Phys. Rev. Lett., 78 (1997), p. 2690
[3] Phys. Rev. E, 56 (1997), p. 5018
[4] Acc. Chem. Res., 120 (2002), p. 5946 For pedagogical derivations of Eq. (1) and related results, see for instance Section 7.4.1 of Understanding Molecular Simulation: from Algorithms to Applications or or
[5] Phys. Rev. E, 60 (1999), p. 2721
[6] Phys. Rev. E, 61 (2000), p. 2361
[7] Proc. Nat. Acad. Sci., 98 (2001), p. 3658
[8] et al. Science, 296 (2002), p. 1832
[9] Europhys. Lett., 70 (2005), p. 593
[10] et al. Nature, 437 (2005), p. 231
[11] et al. Phys. Rev. Lett., 96 (2006), p. 070603
[12] C.H. Kiang, N. Harris, in preparation
[13] Sov. Phys. JETP, 72 (1977), p. 238
[14] Sov. Phys. JETP, 76 (1979), p. 1071
[15] Physica A, 106 (1981), p. 443
[16] Physica A, 106 (1981), p. 480
[17] Fundamentals of Physics, John Wiley and Sons, 2005
[18] Elementary Principles in Statistical Mechanics, Scribner's, New York, 1902 (pp. 42–44)
[19] E. Schrödinger's, Statistical Thermodynamics, Cambridge, 1962. See the paragraphs found between Eqs. (2.13) and (2.14)
[20] Lectures in Statistical Mechanics, Amer. Math. Soc., Providence, 1963 (Chapter I, Section 7)
[21] J. Chem. Phys., 22 (1954), p. 1420
[22] (P. Garbaczewski; R. Olkiewicz, eds.), Lecture Notes in Physics, vol. 597, Springer Verlag, Berlin, 2002
[23] Classical Mechanics, Addison–Wesley, Reading, MA, 1980 (Chapter 9.5)
[24] J. Chem. Phys., 124 (2006), p. 144111
[25] J. Stat. Mech.: Theor. Exp. (2004), p. P07006
[26] Mol. Phys., 103 (2005), p. 2923
[27] | arXiv
[28] Phys. Rev. Lett., 71 (1993), pp. 2401-2404
[29] Phys. Rev. E, 50 (1994), p. 1645
[30] Phys. Rev. Lett., 74 (1995), pp. 2694-2697
[31] J. Phys. A, 31 (1998), p. 3719
[32] J. Stat. Phys., 95 (1999), p. 333
[33] Adv. Phys., 51 (2002), p. 1529 (See also numerous references in)
[34] Helv. Phys. Acta, 51 (1978), p. 202
[35] Phys. Rep., 88 (1982), p. 207
[36] Acc. Chem. Res., 34 (2001), p. 607
[37] J. Phys. Chem. B, 107 (2003), p. 14007
[38] J. Phys. A, 37 (2004), p. 63
[39] Phys. Rev. E, 71 (2005), p. 036126
[40] Phys. Rev., 91 (1953), p. 1505
[41] (personal correspondence and) | arXiv
[42] Phys. Rev. Lett., 96 (2006), p. 050601 Recently Eq. (60) has been recovered as the limiting case of an analogous microcanonical result, derived within a Hamiltonian formulation; see
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