Comparison of far-from-equilibrium work relations

Abstract 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. To cite this article: C. Jarzynski, C. R. Physique 8 (2007).

[1]  C. Jarzynski.  Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach , 1997, cond-mat/9707325.

[2]  K. Schulten,et al.  Calculating potentials of mean force from steered molecular dynamics simulations. , 2004, The Journal of chemical physics.

[3]  Work distribution functions in polymer stretching experiments. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Bryant S. Fujimoto,et al.  Equalities for the Nonequilibrium Work Transferred from an External Potential to a Molecular System. Analysis of Single-Molecule Extension Experiments , 2003 .

[5]  Evans,et al.  Probability of second law violations in shearing steady states. , 1993, Physical review letters.

[6]  Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential. , 2005, Physical review letters.

[7]  G. Hummer,et al.  Free energy reconstruction from nonequilibrium single-molecule pulling experiments , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Artur B Adib.  Free energy surfaces from nonequilibrium processes without work measurement. , 2006, The Journal of chemical physics.

[9]  Y. Kuzovlev,et al.  Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics , 1981 .

[10]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[11]  G. W. Ford,et al.  Lectures in statistical mechanics , 1963 .

[12]  Peter Hänggi,et al.  Stochastic processes: Time evolution, symmetries and linear response , 1982 .

[13]  R. Zwanzig.  High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases , 1954 .

[14]  E. Cohen,et al.  A note on the Jarzynski equality , 2004 .

[15]  C Van den Broeck,et al.  Fluctuation and dissipation of work in a Joule experiment. , 2006, Physical review letters.

[16]  Irwin Oppenheim,et al.  Statistical Mechanical Theory of Transport Processes. VII. The Coefficient of Thermal Conductivity of Monatomic Liquids , 1954 .

[17]  G. Crooks.  Path-ensemble averages in systems driven far from equilibrium , 1999, cond-mat/9908420.

[18]  F. Ritort,et al.  The nonequilibrium thermodynamics of small systems , 2005 .

[19]  H. C. Corben,et al.  Classical Mechanics (2nd ed.) , 1961 .

[20]  J. Gibbs.  Elementary Principles in Statistical Mechanics , 1902 .

[21]  J. Lebowitz,et al.  A Gallavotti–Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics , 1998, cond-mat/9811220.

[22]  Mark A. Miller,et al.  Why is it so difficult to simulate entropies, free energies, and their differences? , 2001, Accounts of chemical research.

[23]  Y. Kuzovlev,et al.  Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: II. Kinetic potential and variational principles for nonlinear irreversible processes , 1981 .

[24]  Cohen,et al.  Dynamical Ensembles in Nonequilibrium Statistical Mechanics. , 1994, Physical review letters.

[25]  Evans,et al.  Equilibrium microstates which generate second law violating steady states. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

[27]  Gerhard Hummer,et al.  Free energy surfaces from single-molecule force spectroscopy. , 2005, Accounts of chemical research.

[28]  C. Jarzynski,et al.  Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies , 2005, Nature.

[29]  Debra J. Searles,et al.  The Fluctuation Theorem , 2002 .

[30]  F. Douarche,et al.  An experimental test of the Jarzynski equality in a mechanical experiment , 2005 .

[31]  Jorge Kurchan,et al.  Fluctuation theorem for stochastic dynamics , 1998 .

[32]  I. Tinoco,et al.  Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality , 2002, Science.

[33]  Reexamination of experimental tests of the fluctuation theorem , 2003, cond-mat/0307148.

[34]  G. Crooks.  Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[36]  Lars Onsager,et al.  Fluctuations and Irreversible Processes , 1953 .

[37]  The Jarzynski equality and the Boltzmann factor , 2005 .