Efficient characterisation of large deviations using population dynamics

We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. Using the simple symmetric exclusion process as a prototypical example, we investigate the convergence of the results with respect to the algorithmic parameters, focussing on the dynamical phase transition between homogeneous and inhomogeneous states, where convergence is relatively difficult to achieve. We discuss how the performance of the algorithm can be optimised, and how it can be efficiently exploited on parallel computing platforms.

[1]  Peter Sollich,et al.  Large deviations and ensembles of trajectories in stochastic models , 2009, 0911.0211.

[2]  Esteban Guevara Hidalgo,et al.  Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time. , 2017, Physical review. E.

[3]  Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy materials. , 2006, The Journal of chemical physics.

[4]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[5]  G. Huber,et al.  Weighted-ensemble Brownian dynamics simulations for protein association reactions. , 1996, Biophysical journal.

[6]  Hugo Touchette,et al.  Nonequilibrium Markov Processes Conditioned on Large Deviations , 2014, 1405.5157.

[7]  Jorge Kurchan,et al.  Direct evaluation of large-deviation functions. , 2005, Physical review letters.

[8]  Jeffrey K Weber,et al.  Emergence of glass-like behavior in Markov state models of protein folding dynamics. , 2013, Journal of the American Chemical Society.

[9]  G. Meehl,et al.  Climate extremes: observations, modeling, and impacts. , 2000, Science.

[10]  H. Touchette.  The large deviation approach to statistical mechanics , 2008, 0804.0327.

[11]  Pedro L. Garrido,et al.  Thermodynamics of Currents in Nonequilibrium Diffusive Systems: Theory and Simulation , 2013, 1312.1246.

[12]  P. R. ten Wolde,et al.  Sampling rare switching events in biochemical networks. , 2004, Physical review letters.

[13]  B Derrida,et al.  Distribution of current in nonequilibrium diffusive systems and phase transitions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Freddy Bouchet,et al.  Population-dynamics method with a multicanonical feedback control. , 2016, Physical review. E.

[15]  V. Lecomte,et al.  Finite Size Scaling of the Dynamical Free-Energy in a Kinetically Constrained Model , 2011, 1111.6394.

[16]  Daniel M Zuckerman,et al.  The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures. , 2008, The Journal of chemical physics.

[17]  J. P. Garrahan,et al.  First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories , 2008, 0810.5298.

[18]  Vivien Lecomte,et al.  A numerical approach to large deviations in continuous time , 2007 .

[19]  C Appert-Rolland,et al.  Universal cumulants of the current in diffusive systems on a ring. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Philipp A. Hoehn,et al.  Quantum theory from questions , 2015, 1511.01130.

[21]  James B. Anderson,et al.  A random‐walk simulation of the Schrödinger equation: H+3 , 1975 .

[22]  David T. Limmer,et al.  Importance sampling large deviations in nonequilibrium steady states. I. , 2017, The Journal of chemical physics.

[23]  P. Grassberger.  Go with the Winners: a General Monte Carlo Strategy , 2002, cond-mat/0201313.

[24]  Simulation of large deviation functions using population dynamics , 2008, 0811.1041.

[25]  R. Jack,et al.  Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model. , 2016, Physical review letters.

[26]  B. Derrida,et al.  of Statistical Mechanics : Theory and Experiment Non-equilibrium steady states : fluctuations and large deviations of the density and of the current , 2007 .

[27]  J P Garrahan,et al.  Dynamical first-order phase transition in kinetically constrained models of glasses. , 2007, Physical review letters.

[28]  Validity of one-dimensional QED for a system with spatial symmetry , 2015, 1506.02710.

[29]  T. Speck,et al.  Experimental Evidence for a Structural-Dynamical Transition in Trajectory Space. , 2016, Physical review letters.

[30]  S. R. Clark,et al.  Capturing exponential variance using polynomial resources: applying tensor networks to nonequilibrium stochastic processes. , 2014, Physical review letters.

[31]  P. Gretener.  Significance of the Rare Event in Geology , 1967 .

[32]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[33]  F. van Wijland,et al.  Dynamic transition in an atomic glass former: A molecular-dynamics evidence , 2011, 1105.2460.

[34]  J. P. Garrahan,et al.  Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains. , 2017, Physical review. E.

[35]  A. B. Bortz,et al.  A new algorithm for Monte Carlo simulation of Ising spin systems , 1975 .

[36]  V. Lecomte,et al.  Dynamical Symmetry Breaking and Phase Transitions in Driven Diffusive Systems. , 2016, Physical review letters.

[37]  David Chandler,et al.  Transition path sampling: throwing ropes over rough mountain passes, in the dark. , 2002, Annual review of physical chemistry.

[38]  T. Bodineau,et al.  Cumulants and large deviations of the current through non-equilibrium steady states , 2007, 0704.2726.

[39]  P. Hurtado,et al.  Current fluctuations and statistics during a large deviation event in an exactly solvable transport model , 2008, 0810.5543.

[40]  Jeffrey K Weber,et al.  Dynamical phase transitions reveal amyloid-like states on protein folding landscapes. , 2014, Biophysical journal.

[41]  J. P. Garrahan,et al.  Dynamic Order-Disorder in Atomistic Models of Structural Glass Formers , 2009, Science.

[42]  J. P. Garrahan,et al.  Inactive dynamical phase of a symmetric exclusion process on a ring , 2012, 1203.1600.

[43]  T. Speck,et al.  First-order phase transition in a model glass former: coupling of local structure and dynamics. , 2012, Physical review letters.

[44]  F. Bouchet,et al.  Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes , 2015, Annales Henri Poincaré.

[45]  Jorge Kurchan,et al.  Probing rare physical trajectories with Lyapunov weighted dynamics , 2007 .

[46]  Cristian S. Calude,et al.  Value-indefinite observables are almost everywhere , 2013, 1309.7188.