Population-dynamics method with a multicanonical feedback control

Abstract

We discuss the Giardinà-Kurchan-Peliti population dynamics method for evaluating large deviations of time-averaged quantities in Markov processes [Phys. Rev. Lett. 96, 120603 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.120603]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dynamical phase transitions. We show how these errors can be mitigated by introducing control forces within the algorithm. These forces are determined by an iteration-and-feedback scheme, inspired by multicanonical methods in equilibrium sampling. We demonstrate substantially improved results in a simple model, and we discuss potential applications to more complex systems.

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

“…By repeating this procedure, one can optimize the choice of the control potential (see Refs. [30] and [40] for details).…”

“…To this end, we generalize a recently proposed adaptive method [30] to Markov jump processes. The method is based on a cloning algorithm [19,33] that uses a population of N c clones (or copies) of the system.…”

“…In this step, each clone a generates a number of offspring proportional to its weight γ a . The mean activity hKi s can then be obtained as the average of K a ðτÞ over the final population [30].…”

“…To avoid this issue, we combine the existing cloning algorithm [13,[19][20][21][22]33,34] with a modification of the dynamics [35][36][37][38], following Ref. [30]. In order to aid sampling of trajectories with nontypical activity, we modify the transition rates of the model as…”

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

“…An important observation is that the bounds on fluctuations of a counting observable and its FPTs are controlled by the average dynamical activity, in analogy to the role played by the entropy production in the case of currents [1,13]. We hope these results will add to the growing body of work applying large deviation ideas and methods to the study of dynamics in driven systems [29][30][31][32][33][34][35][36][37][38][39][40][41], glasses [25,[42][43][44][45][46][47], protein folding and signaling networks [48][49][50][51], open quantum systems [52][53][54][55][56][57][58][59][60][61][62][63][64], and many other problems in nonequilibrium [65][66][67][68][69][70][71][72].…”