The nonequilibrium thermodynamics of small systems

Felix Ritort

doi:10.1016/j.crhy.2007.04.018

The nonequilibrium thermodynamics of small systems
[La thermodynamique de non-équilibre des petits systèmes]

Felix Ritort ^1,²

¹ Department de Fisica Fonamental, Faculty of Physics, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
² CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Sanidad Carlos III C/Sinesio Delgado 6, Madrid, Spain

Comptes Rendus. Physique, Volume 8 (2007) no. 5-6, pp. 528-539.

Résumé
Abstract

La thermodynamique de non-équilibre des petits systèmes décrit les processus d'échanges d'énergie entre un système et son environnement dans le domaine des basses énergies de quelques $k_{B} T$ où les fluctuations browniennes sont dominantes. Le but principal de cette discipline est d'identifier les blocs de construction d'une théorie générale décrivant les fluctuations d'énergie dans les processus de non-équilibre se produisant dans des systèmes s'étendant depuis la physique de la matière condensée jusqu'à la biophysique. Dans cet article, je discute quelques aspects des théorèmes de fluctuations et de la thermodynamique des chemins qui nécessitent une meilleure compréhension des grandes déviations en physique statistique de non-équilibre. Je montre aussi comment les expériences sur des molécules individuelles constituent une précieuse source de connaissance et d'information qui peut contribuer grandement à dévoiler les questions les plus importantes et pertinentes dans ce passionnant domaine de recherche.

Nonequilibrium thermodynamics of small systems describes energy exchange processes between a system and its environment in the low energy range of a few $k_{B} T$ where Brownian fluctuations are dominant. The main goal of this discipline is to identify the building blocks of a general theory describing energy fluctuations in nonequilibrium processes occurring in systems ranging from condensed matter physics to biophysics. In this article I discuss some aspects about fluctuation theorems and path thermodynamics that call for the necessity of a better understanding of large deviations in nonequilibrium statistical physics. I also emphasize how single molecule experiments are a valuable source of knowledge and information that can greatly contribute to the unveiling of the most important and relevant questions in this exciting field of research.

Reçu le : 2007-03-26
Publié le : 2007-06-01

DOI : 10.1016/j.crhy.2007.04.018

Keywords: Nonequilibrium thermodynamics, Single molecule experiments, Molecular biophysics
Mot clés : Thermodynamique de non-équilibre, Expériences sur des molécules individuelles, Biophysique moléculaire

Affiliations des auteurs :

Felix Ritort ^{1, 2}

@article{CRPHYS_2007__8_5-6_528_0,
     author = {Felix Ritort},
     title = {The nonequilibrium thermodynamics of small systems},
     journal = {Comptes Rendus. Physique},
     pages = {528--539},
     publisher = {Elsevier},
     volume = {8},
     number = {5-6},
     year = {2007},
     doi = {10.1016/j.crhy.2007.04.018},
     language = {en},
}

TY  - JOUR
AU  - Felix Ritort
TI  - The nonequilibrium thermodynamics of small systems
JO  - Comptes Rendus. Physique
PY  - 2007
SP  - 528
EP  - 539
VL  - 8
IS  - 5-6
PB  - Elsevier
DO  - 10.1016/j.crhy.2007.04.018
LA  - en
ID  - CRPHYS_2007__8_5-6_528_0
ER  -

%0 Journal Article
%A Felix Ritort
%T The nonequilibrium thermodynamics of small systems
%J Comptes Rendus. Physique
%D 2007
%P 528-539
%V 8
%N 5-6
%I Elsevier
%R 10.1016/j.crhy.2007.04.018
%G en
%F CRPHYS_2007__8_5-6_528_0

Felix Ritort. The nonequilibrium thermodynamics of small systems. Comptes Rendus. Physique, Volume 8 (2007) no. 5-6, pp. 528-539. doi : 10.1016/j.crhy.2007.04.018. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.04.018/

Bibliographie
Cité par

[1] C. Bustamante; J. Liphardt; F. Ritort The nonequilibrium thermodynamics of small systems, Physics Today, Volume 58 (2005), pp. 43-48

[2] F. Ritort, Nonequilibrium fluctuations in small systems: From physics to biology, Advances in Chemical Physics 137 (2007), in press

[3] J. Howard Mechanics of Motor Proteins and the Cytoskeleton, Sinauer, Sunderland, MA, 2001

[4] R.D. Astumian Thermodynamics and kinetics of a Brownian motor, Science, Volume 276 (1997), pp. 917-922

[5] F. Ritort Single molecule experiments in biological physics: methods and applications, Journal of Physics (Condensed Matter), Volume 18 (2006), p. R531-R583

[6] C.K. Mathews; K.E. van Holde; K.G. Ahern Biochemistry, Addison–Wesley Publishing Company, 2000

[7] H. Wang; G. Oster The Stokes efficiency for molecular motors and its applications, Europhysics Letters, Volume 57 (2002), pp. 134-140

[8] C. Bustamante; Y.R. Chemla; N.R. Forde; D. Izhaky Mechanical processes in biochemistry, Annual Reviews of Biochemistry, Volume 73 (2004), pp. 705-748

[9] H. Yin; M.D. Wang; K. Svoboda; R. Landick; S.M. Block; J. Gelles Transcription against an applied force, Science, Volume 270 (1995), pp. 1653-1657

[10] M.D. Wang; M.J. Schnitzer; H. Yin; R. Landick; J. Gelles; S.M. Block Force and velocity measured for single molecules of RNA polymerase, Science, Volume 282 (1998), pp. 902-907

[11] R.J. Davenport; G.J. Wuite; R. Landick; C. Bustamante Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase, Science, Volume 287 (2000), pp. 2497-2500

[12] N.R. Forde; D. Izhaky; G.R. Woodcock; G.J.L. Wuite; C. Bustamante Using mechanical force to probe the mechanism of pausing and arrest during continuous elongation by Escherichia coli RNA polymerase, Proceedings of the National Academy of Sciences, Volume 99 (2002), pp. 11682-11687

[13] R. Kawai; J.M.R. Parrondo; C.V. den Broeck Dissipation: the phase-space perspective, Physical Review Letters, Volume 98 (2007), p. 080602

[14] D.J. Evans; D.J. Searles Equilibrium microstates which generate second law violating steady-states, Physical Review E, Volume 50 (1994), pp. 1645-1648

[15] E.G.D. Cohen; D.J. Evans; G.P. Morriss Probability of second law violations in shearing steady states, Physical Review Letters, Volume 71 (1993), pp. 2401-2404

[16] G. Gallavotti; E.G.D. Cohen Dynamical ensembles in nonequilibrium statistical mechanics, Physical Review Letters, Volume 74 (1995), pp. 2694-2697

[17] J. Kurchan Fluctuation theorem for stochastic dynamics, Journal of Physics A, Volume 31 (1998), pp. 3719-3729

[18] J.L. Lebowitz; H. Spohn A Gallavotti–Cohen type symmetry in the large deviation functional for stochastic dynamics, Journal of Statistical Physics, Volume 95 (1999), pp. 333-365

[19] C. Maes The fluctuation theorem as a Gibbs property, Journal of Statistical Physics, Volume 95 (1999), pp. 367-392

[20] P. Gaspard Fluctuation theorem for nonequilibrium reactions, Journal of Chemical Physics, Volume 120 (2004), pp. 8898-8905

[21] U. Seifert Entropy production along a stochastic trajectory and an integral fluctuation theorem, Physical Review Letters, Volume 95 (2005), p. 040602

[22] C. Jarzynski Nonequilibrium equality for free-energy differences, Physical Review Letters, Volume 78 (1997), pp. 2690-2693

[23] G.E. Crooks Entropy production fluctuation theorem and the nonequilibrium work relation for free-energy differences, Physical Review E, Volume 60 (1999), pp. 2721-2726

[24] G.E. Crooks Path-ensemble averages in systems driven far from equilibrium, Physical Review E, Volume 61 (2000), pp. 2361-2366

[25] D. Astumian Equilibrium theory for a particle pulled by a moving optical trap, Journal of Chemical Physics, Volume 126 (2007), p. 111102

[26] B. Cleuren; C. Van den Broeck; R. Kawai Fluctuation and dissipation of work in a Joule experiment, Physical Review Letters, Volume 96 (2006), p. 050601

[27] F. Ritort; C. Bustamante; I. Tinoco A two-state kinetic model for the unfolding of single molecules by mechanical force, Proceedings of the National Academy of Sciences, Volume 99 (2002), pp. 13544-13548

[28] F. Ritort Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism, Journal of Statistical Mechanics (Theor. Exp.) (2004), p. P10016

[29] C. Jarzynski Rare events and the convergence of exponentially averaged work values, Physical Review E, Volume 73 (2006), p. 046105

[30] A. Imparato; L. Peliti Work distribution and path integrals in mean-field systems, Europhysics Letters, Volume 70 (2005), pp. 740-746

[31] A. Imparato; L. Peliti Work probability distribution in systems driven out of equilibrium, Physical Review E, Volume 72 (2005), p. 046114

[32] P. Hanggi; P. Talkner; M. Borkovec Reaction-rate theory: fifty years after Kramers, Review of Modern Physics, Volume 62 (1990), pp. 251-341

[33] V.I. Melnikov The Kramers problem: fifty years of development, Physics Reports, Volume 209 (1991), pp. 1-71

[34] E. Evans Probing the relationship between force—lifetime—and chemistry in single molecular bonds, Annual Reviews of Biophysics and Biomolecular Structure, Volume 30 (2001), pp. 105-128

[35] E. Evans; P. Williams Dynamic force spectroscopy (H. Flyvbjerg; F. Jülicher; P. Ormos; F. David, eds.), Physics of Biomolecules and Cells, vol. LXXV, Springer-Verlag, Berlin, 2002, pp. 145-204

[36] F. Ritort Spontaneous relaxation in generalized models for glassy dynamics, Journal of Physical Chemistry B, Volume 108 (2004), pp. 6893-6900

[37] J. Liphardt; B. Onoa; S.B. Smith; I. Tinoco; C. Bustamante Reversible unfolding of single RNA molecules by mechanical force, Science, Volume 292 (2001), pp. 733-737

[38] J. Liphardt; S. Dumont; S.B. Smith; I. Tinoco; C. Bustamante Equilibrium information from nonequilibrium measurements in an experimental test of the Jarzynski equality, Science, Volume 296 (2002), pp. 1833-1835

[39] D. Collin; F. Ritort; C. Jarzynski; S.B. Smith; I. Tinoco; C. Bustamante Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies, Nature, Volume 437 (2005), pp. 231-234

[40] B. Derrida; J.L. Lebowitz; E.R. Speer Free energy functional for nonequilibrium systems: an exactly solvable case, Physical Review Letters, Volume 87 (2001), p. 150601

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Work and heat probability distributions in out-of-equilibrium systems

Alberto Imparato; Luca Peliti

C. R. Phys (2007)

Comparison of far-from-equilibrium work relations

Christopher Jarzynski

C. R. Phys (2007)