Nonlinear transport coefficients from large deviation functions

Gao, Chloe Y.; Limmer, David T.

doi:10.1063/1.5110507

Cited by 36 publications

(36 citation statements)

References 60 publications

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“…where the excess heat Q = ∆U λ [X(t)|x(0)] − ∆U λ [X(t)|x(0)] is odd under time reversal, and the excess dynamical activity Γ = ∆U λ [X(t)|x(0)] + ∆U λ [X(t)|x(0)] is even. On the whole, both the heat and the activity play important roles in response and stability of nonequilibrium systems (14,15). While the heat has a simple mechanical definition and is largely independent of the system's dynamics, the activity depends on details of the equation of motion, making it hard to generalize.…”

Section: Stochastic Thermodynamics Of Rate Enhancementmentioning

confidence: 99%

Dissipation bounds the amplification of transition rates far from equilibrium

Kuznets-Speck

Limmer

2021

Proc. Natl. Acad. Sci. U.S.A.

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Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long-lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general framework to relate the enhancement of a transition rate to the energy dissipated or to bound the enhancement achievable for a given energy expenditure. We employ recent advances in stochastic thermodynamics to build such a framework, which can be used to gain mechanistic insight into transitions far from equilibrium. We show that under general conditions, there is a basic speed limit relating the typical excess heat dissipated throughout a transition and the rate amplification achievable. We illustrate this tradeoff in canonical examples of diffusive barrier crossings in systems driven with autonomous and deterministic external forcing protocols. In both cases, we find that our speed limit tightly constrains the rate enhancement.

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Section: Stochastic Thermodynamics Of Rate Enhancementmentioning

confidence: 99%

Dissipation bounds the amplification of transition rates far from equilibrium

Kuznets-Speck

Limmer

2021

Proc. Natl. Acad. Sci. U.S.A.

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“…Tuning the parameters ζ thus promotes trajectories that have as typical exchanges ∆ τ * . This approach has been employed to study dynamic phase transitions [27] in the Ising model [87,88], glasses [89][90][91][92], quantum systems [93], and to extract nonlinear transport coefficients [94]. Since rate functions encode rare fluctuations they are difficult to compute directly in numerical simulations.…”

Section: Challengesmentioning

confidence: 99%

Modeling of biomolecular machines in non-equilibrium steady states

Speck

2021

Preprint

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Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with ten thousands or even millions degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared towards the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.

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“…In molecular systems, rare events determine the rates by which chemical reactions occur and phases interconvert, 5 and they also encode the response of systems driven to flow or unfold. [6][7][8][9][10] Strategies that afford a means of studying rare dynamical events in statistically unbiased ways are particularly desired, in order to deduce the intrinsic pathways by which they occur and to evaluate their likelihoods. Borrowing notions from reinforcement learning, 11 we have developed a method to generate rare dynamical trajectories directly through the optimization of an auxiliary dynamics that generates an ensemble of trajectories with the correct relative statistical weights.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement learning of rare diffusive dynamics

Das

Rose

Garrahan

et al. 2021

The Journal of Chemical Physics

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We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, like those relevant in the study of reactive events, as well as trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, like those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.

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Nonlinear transport coefficients from large deviation functions

Cited by 36 publications

References 60 publications

Dissipation bounds the amplification of transition rates far from equilibrium

Dissipation bounds the amplification of transition rates far from equilibrium

Modeling of biomolecular machines in non-equilibrium steady states

Reinforcement learning of rare diffusive dynamics

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