Abstract
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.
Similar content being viewed by others
References
R. Assaraf, M. Caffarel and A. Khelif, Diffusion Monte Carlo with a fixed number of walkers. Phys. Rev. E 61(4):4566–4575 (2000).
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).
E. Cancès, F. Legoll and G. Stoltz, Theoretical and numerical comparison of sampling methods for molecular dynamics. IMA Preprint 2040 (2005).
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).
P. Del Moral, Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications, Springer Series Probability and its Applications (Springer, 2004).
P. Del Moral, A. Doucet and G. W. Peters, Sequential Monte Carlo samplers, Preprint version, available on request at the URL http://www.cs.ubc.ca/∼arnaud/(2004).
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).
A. Doucet, N. de Freitas and N. J. Gordon, Sequential Monte Carlo Methods in Practice, Series Statistics for Engineering and Information Science (Springer, 2001).
A. Doucet, M. Rousset, Time continuous limit of sequential samplers, in preparation.
M. I. Freidlin and A. D. Wentzell, Random perturbations of dynamical systems, second edition (Springer-Verlag, 1998).
D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic Press, 2002).
D. A. Hendrix and C. Jarzynski, A “fast growth” method of computing free energy differences. J. Chem. Phys. 114(14):5974–5981 (2001).
K. Hukushima and Y. Iba, Population annealing and its application to a spin glass. AIP Conference Proceedings 690(1):200–206 (2003).
G. Hummer. and A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments. PNAS 98(7):3658–3661 (2001).
Y. Iba, Extended ensemble Monte Carlo. Int. J. Mod. Phys. C 12:623–656 (2001).
C. Jarzynski, Equilibrium free energy differences from nonequilibrium measurements: A master equation approach. Phys. Rev. E 56(5):5018–5035 (1997).
C. Jarzynski, Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78(14):2690–2693 (1997).
S. Kirkpatrick, C. G. Gelatt and M. P. Vecchi, Optimization by simulated annealing. Science. 220:671–680 (1983).
J. G. Kirkwood, Statistical mechanics of fluid mixtures. J. Chem. Phys. 3:300–313 (1935).
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).
E. Marinari and G. Parisi, Simulated tempering: A new Monte Carlo scheme. Europhys. Lett. 19:451–458 (1992).
R. Neal, Annealing importance sampling. Statistics and Computing 11(2):125–139 (2001).
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).
J. M. Rickman and R. LeSar, Free-energy calculations in materials research. Annu. Rev. Matter. Res. 32:195–217 (2002).
M. Rousset, On the control of an Interacting Particle estimation of Schrödinger groundstates, Preprint, available at the URL www.Isp.ups-tlse.fr/Fp/Rousset/article3.pdf
M. Rousset and G. Stoltz, An interacting particle system approach for molecular dynamics. Rapport de recherche CERMICS 283 (2005).
M. Rousset Phd Thesis, in preparation.
G. Stoltz Phd Thesis, in preparation.
S. Sun, Equilibrium free energies from path sampling of nonequilibrium trajectories. J. Chem. Phys. 118(13):5769–5775 (2003).
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).
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).
R. Zwanzig, High-temperature equation of state by a perturbation method: I. Nonpolar gases. J. Chem. Phys. 22:1420–1426 (1954).
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS: 65C05 65C35 80A10
Rights and permissions
About this article
Cite this article
Rousset, M., Stoltz, G. Equilibrium Sampling From Nonequilibrium Dynamics. J Stat Phys 123, 1251–1272 (2006). https://doi.org/10.1007/s10955-006-9090-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-006-9090-2