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Equilibrium Sampling From Nonequilibrium Dynamics

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We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a nonequilibrium random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual nonequilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths.

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  1. R. Assaraf, M. Caffarel and A. Khelif, Diffusion Monte Carlo with a fixed number of walkers. Phys. Rev. E 61(4):4566–4575 (2000).

    Article  ADS  Google Scholar 

  2. A. Brünger, C. B. Brooks and M. Karplus, Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Lett. 105:495–500 (1983).

    Article  ADS  Google Scholar 

  3. E. Cancès, F. Legoll and G. Stoltz, Theoretical and numerical comparison of sampling methods for molecular dynamics. IMA Preprint 2040 (2005).

  4. E. A. Carter, G. Ciccotti, J. T. Hynes and R. Kapral, Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 156:472–477 (1989).

    Article  ADS  Google Scholar 

  5. P. Del Moral, Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications, Springer Series Probability and its Applications (Springer, 2004).

  6. P. Del Moral, A. Doucet and G. W. Peters, Sequential Monte Carlo samplers, Preprint version, available on request at the URL∼arnaud/(2004).

  7. P. Del Moral and L. Miclo, Branching and Interacting Particle Systems approximations of Feynman -Kac formulae with applications to nonlinear filtering, Séminaire de Probabilités XXXI. Lecture notes in Mathematics 1729:1–145 (2000).

    Article  Google Scholar 

  8. A. Doucet, N. de Freitas and N. J. Gordon, Sequential Monte Carlo Methods in Practice, Series Statistics for Engineering and Information Science (Springer, 2001).

  9. A. Doucet, M. Rousset, Time continuous limit of sequential samplers, in preparation.

  10. M. I. Freidlin and A. D. Wentzell, Random perturbations of dynamical systems, second edition (Springer-Verlag, 1998).

  11. D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic Press, 2002).

  12. D. A. Hendrix and C. Jarzynski, A “fast growth” method of computing free energy differences. J. Chem. Phys. 114(14):5974–5981 (2001).

    Article  ADS  Google Scholar 

  13. K. Hukushima and Y. Iba, Population annealing and its application to a spin glass. AIP Conference Proceedings 690(1):200–206 (2003).

    Article  ADS  Google Scholar 

  14. G. Hummer. and A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments. PNAS 98(7):3658–3661 (2001).

    Article  PubMed  ADS  Google Scholar 

  15. Y. Iba, Extended ensemble Monte Carlo. Int. J. Mod. Phys. C 12:623–656 (2001).

    Article  ADS  Google Scholar 

  16. C. Jarzynski, Equilibrium free energy differences from nonequilibrium measurements: A master equation approach. Phys. Rev. E 56(5):5018–5035 (1997).

    Article  ADS  Google Scholar 

  17. C. Jarzynski, Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78(14):2690–2693 (1997).

    Article  ADS  Google Scholar 

  18. S. Kirkpatrick, C. G. Gelatt and M. P. Vecchi, Optimization by simulated annealing. Science. 220:671–680 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  19. J. G. Kirkwood, Statistical mechanics of fluid mixtures. J. Chem. Phys. 3:300–313 (1935).

    Article  ADS  Google Scholar 

  20. T. Lelièvre, M. Rousset and G. Stoltz, Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case, arXiv preprint (condmat/0603426) (2006).

  21. E. Marinari and G. Parisi, Simulated tempering: A new Monte Carlo scheme. Europhys. Lett. 19:451–458 (1992).

    Article  ADS  Google Scholar 

  22. R. Neal, Annealing importance sampling. Statistics and Computing 11(2):125–139 (2001).

    Article  MathSciNet  Google Scholar 

  23. H. Oberhofer, C. Dellago and P. L. Geissler, Biased sampling of non-equilibrium trajectories: Can fast switching simulations outperform conventional free energy calculation methods? J. Chem. Phys. B 109:6902–6915 (2005).

    Article  Google Scholar 

  24. J. M. Rickman and R. LeSar, Free-energy calculations in materials research. Annu. Rev. Matter. Res. 32:195–217 (2002).

    Article  Google Scholar 

  25. M. Rousset, On the control of an Interacting Particle estimation of Schrödinger groundstates, Preprint, available at the URL

  26. M. Rousset and G. Stoltz, An interacting particle system approach for molecular dynamics. Rapport de recherche CERMICS 283 (2005).

  27. M. Rousset Phd Thesis, in preparation.

  28. G. Stoltz Phd Thesis, in preparation.

  29. S. Sun, Equilibrium free energies from path sampling of nonequilibrium trajectories. J. Chem. Phys. 118(13):5769–5775 (2003).

    Article  ADS  Google Scholar 

  30. G. M. Torrie and J. P. Valleau, Nonphysical sampling distributions in Monte-Carlo free energy estimation: Umbrella sampling. J. Comp. Phys. 23:187–199 (1977).

    Article  ADS  Google Scholar 

  31. F. M. Ytreberg and D. M. Zuckerman, Single-ensemble nonequilibrium path sampling estimates of free energy differences. J. Chem. Phys. 120(3):10876–10879 (2004).

    Article  PubMed  ADS  Google Scholar 

  32. R. Zwanzig, High-temperature equation of state by a perturbation method: I. Nonpolar gases. J. Chem. Phys. 22:1420–1426 (1954).

    Article  ADS  Google Scholar 

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Correspondence to Mathias Rousset.

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AMS: 65C05 65C35 80A10

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Rousset, M., Stoltz, G. Equilibrium Sampling From Nonequilibrium Dynamics. J Stat Phys 123, 1251–1272 (2006).

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