Adaptive Sampling of Large Deviations

Ferré, Grégoire; Touchette, Hugo

doi:10.1007/s10955-018-2108-8

Cited by 61 publications

(73 citation statements)

References 64 publications

(179 reference statements)

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“…This is because, for the parameters considered in our numerical study, heat fluctuates much more than work, as already suggested by the moments and cumulants shown in Fig. 6b and c. Let us note that while we have computed the LDFs using the standard BD, which was much more time consuming than the evaluation of the MNM, there are various optimized simulation algorithms [45][46][47] for computing of LDFs that can render BD simulations more competitive.…”

Section: B Moment Generating Functionsmentioning

confidence: 73%

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Physically consistent numerical solver for time-dependent Fokker-Planck equations

2019

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We present a simple thermodynamically consistent method for solving time-dependent Fokker-Planck equations (FPE) for over-damped stochastic processes, also known as Smoluchowski equations. It yields both transition and steady-state behavior and allows for computations of momentgenerating and large-deviation functions of observables defined along stochastic trajectories, such as the fluctuating particle current, heat and work. The key strategy is to approximate the FPE by a Master equation with transition rates in configuration space that obey a local detailed balance condition for arbitrary discretization. Its time-dependent solution is obtained by a direct computation of the time-ordered exponential, representing the propagator of the FPE, by summing over all possible paths in the discretized space. The method thus not only preserves positivity and normalization of the solutions, but also yields a physically reasonable total entropy production, regardless of the discretization. To demonstrate the validity of the method and to exemplify its potential for applications, we compare it against Brownian-dynamics simulations of a heat engine based on an active Brownian particle trapped in a time-dependent quartic potential.

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Section: B Moment Generating Functionsmentioning

confidence: 73%

“…For the parts of the piece-wise constant protocol with time-independent potential, the tilted matrices can also be computed from the formula (47).…”

Section: B Moment Generating Functionsmentioning

confidence: 99%

Physically consistent numerical solver for time-dependent Fokker-Planck equations

2019

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“…In practice, the driving protocol should simply mimic the biased noise realizations. This line of thought has already been exploited for efficient sampling of the biased ensemble [65,[114][115][116], where control forces make rare events become typical. Moreover, since our analytic framework encompasses the case of a specific bias for each pair of particle, it could potentially be regarded as a fruitful route to promote the spontaneous self-assembly of complex structures at the cost of energy dissipation.…”

Section: Discussionmentioning

confidence: 99%

How Dissipation Constrains Fluctuations in Nonequilibrium Liquids: Diffusion, Structure, and Biased Interactions

et al. 2019

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The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials. arXiv:1808.07838v4 [cond-mat.stat-mech]

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“…The obtained results also open a direction of research to characterise fluctuations in a given system by engineering a new system subjected to an additional external force. Such an approach has been used in recent studies on adaptive algorithms, based for instance on a feedback procedure to evaluate the effective force [66,67,68,69], improving the computational efficiency. The weak-noise regime has been seldom studied (it is in fact know to present specific difficulties [66]), and the results we present in this paper could help to understand large-time fluctuations and their associated phenomenology both in experiments and simulations.…”

Section: Discussionmentioning

confidence: 99%

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Tizón-Escamilla¹,

Lecomte²,

Bertin³

2019

J. Stat. Mech.

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In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the observable, that we study through a biased dynamics in a largedeviation framework. We determine explicitly the effective probability-conserving dynamics which makes rare trajectories of the original dynamics become typical trajectories of the effective one. Our approach makes use of a weak-noise path-integral description in which the action is minimised by the rare trajectories of interest. For 'current-type' additive observables, we find the emergence of a propagative trajectory minimising the action for large enough deviations, revealing the existence of a dynamical phase transition at a fluctuating level. In addition, we provide a new method to determine the scaled cumulant generating function of the observable without having to optimise the action. It allows one to show that the weak-noise and the large-time limits commute in this problem. Finally, we show how the biased dynamics can be mapped in practice to an effective driven dynamics, which takes the form of a driven Langevin dynamics in an effective potential. The non-trivial shape of this effective potential is key to understand the link between the dynamical phase transition in the large deviations of current and the standard depinning transition of a particle in a tilted potential. ‡ During the preparation of this manuscript, we became aware that works parallel to ours were completed using similar approaches [22,23].

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Adaptive Sampling of Large Deviations

Cited by 61 publications

References 64 publications

Physically consistent numerical solver for time-dependent Fokker-Planck equations

Physically consistent numerical solver for time-dependent Fokker-Planck equations

How Dissipation Constrains Fluctuations in Nonequilibrium Liquids: Diffusion, Structure, and Biased Interactions

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

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