On the efficiency of path sampling methods for the calculation of free energies from non-equilibrium simulations

According to the Jarzynski theorem, equilibrium free energy differences can be calculated from the statistics of work carried out during non-equilibrium transformations. Although exact, this approach can be plagued with large statistical errors, particularly for systems driven strongly away from equilibrium. Recently, several approaches have been suggested for reducing these errors. In this paper we study the efficiency of these methods using two models for which analytical solutions exist.

[1]  B. Berg,et al.  Multicanonical algorithms for first order phase transitions , 1991 .

[2]  G. Crooks Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems , 1998 .

[3]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

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

[5]  C. Jarzynski Rare events and the convergence of exponentially averaged work values. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Sean X. Sun Equilibrium free energies from path sampling of nonequilibrium trajectories , 2003 .

[7]  D. Zuckerman,et al.  Single-ensemble nonequilibrium path-sampling estimates of free energy differences. , 2004, The Journal of chemical physics.

[8]  P. Hertz,et al.  Über die mechanischen Grundlagen der Thermodynamik , 1910 .

[9]  C. Dellago,et al.  Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods? , 2005, The journal of physical chemistry. B.

[10]  Thomas B Woolf,et al.  Theory of a systematic computational error in free energy differences. , 2002, Physical review letters.

[11]  C. Dellago,et al.  Transition path sampling and the calculation of rate constants , 1998 .

[12]  P. Ehrenfest Adiabatische Invarianten und Quantentheorie , 1916 .

[13]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[14]  C. Dellago,et al.  Equilibrium free energies from fast-switching trajectories with large time steps. , 2005, The Journal of chemical physics.

[15]  C. Geyer,et al.  Annealing Markov chain Monte Carlo with applications to ancestral inference , 1995 .

[16]  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.

[17]  M. Athènes A path-sampling scheme for computing thermodynamic properties of a many-body system in a generalized ensemble , 2004 .

[18]  A. Pohorille,et al.  Free energy calculations : theory and applications in chemistry and biology , 2007 .

[19]  A. Lichtenberg,et al.  Regular and Stochastic Motion , 1982 .

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

[21]  Denis J. Evans,et al.  A non-equilibrium free energy theorem for deterministic systems , 2003 .

[22]  C. Dellago,et al.  A proof of Jarzynski's nonequilibrium work theorem for dynamical systems that conserve the canonical distribution. , 2006, The Journal of chemical physics.

[23]  J. Kirkwood Statistical Mechanics of Fluid Mixtures , 1935 .

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

[25]  F. Ritort,et al.  Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[26]  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.

[27]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[28]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[29]  Christophe Chipot,et al.  Comprar Free Energy Calculations · Theory and Applications in Chemistry and Biology | Chipot, Christophe | 9783540736172 | Springer , 2007 .

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

[31]  Christophe Chipot,et al.  Free Energy Calculations , 2008 .

[32]  A. Grosberg,et al.  Practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example. , 2005, The journal of physical chemistry. B.

[33]  B. Widom,et al.  Some Topics in the Theory of Fluids , 1963 .