- Access by Xinjiang University
Application of importance sampling to the computation of large deviations in nonequilibrium processes
Phys. Rev. E 83, 031119 – Published 16 March, 2011
DOI: https://doi.org/10.1103/PhysRevE.83.031119
Abstract
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track of the relative weight of phase-space trajectories generated by the modified and the original dynamics one can obtain the required probabilities. The algorithm is tested on two model systems of steady-state particle and heat transport where we find a huge improvement from direct simulation methods.
Article Text
References (19)
- D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Phys. Rev. Lett. 71, 2401 (1993); D. J. Evans and D. J. Searles, Phys. Rev. E 50, 1645 (1994); G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995); J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 333 (1999).
- C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004).
- T. Bodineau and B. Derrida, Phys. Rev. Lett. 92, 180601 (2004); C. Enaud and B. Derrida, J. Stat. Phys. 114, 537 (2004).
- B. Derrida, B. Doucot, and P.-E. Roche, J. Stat. Phys. 115, 717 (2004).
- B. Derrida and J. L. Lebowitz, Phys. Rev. Lett. 80, 209 (1998).
- P. Visco, J. Stat. Mech. P06006 (2006).
- K. Saito and A. Dhar, Phys. Rev. Lett. 99, 180601 (2007).
- C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997); G. E. Crooks, Phys. Rev. E 60, 2721 (1999); T. Hatano and S. I. Sasa, Phys. Rev. Lett. 86, 3463 (2001); U. Seifert, ibid. 95, 040602 (2005).
- S. R. S. Varadhan, Large Deviations and Applications (SIAM, Philadelphia, PA, 1984).
- H. Touchette, Phys. Rep. 478, 1 (2009).
- C. Giardina, J. Kurchan, and L. Peliti, Phys. Rev. Lett. 96, 120603 (2006).
- P. I. Hurtado and P. L. Garrido, Phys. Rev. Lett. 102, 250601 (2009); J. Stat. Mech. P02032 (2009).
- J. A. Bucklew, Introduction to Rare Event Simulation (Springer-Verlag, New York, 2004).
- M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys. 23, 356 (1955).
- P. Grassberger, Phys. Rev. E 56, 3682 (1997).
- O. Mazonka, C. Jarzyski, and J. Bocki, Nucl. Phys. A 641, 335 (1998).
- C. Dellago, P. G. Bolhuis, F. S. Csajka, and D. Chandler, J. Chem. Phys. 108, 1964 (1998).
- R. J. Allen, P. B. Warren, and P. R. ten Wolde, Phys. Rev. Lett. 94, 018104 (2005).
- F. van Wijland, Phys. Rev. E 74, 063101 (2006).