Hyperuniformity and Phase Separation in Biased Ensembles of Trajectories for Diffusive Systems

Jack, Robert L.; Thompson, Ian R.; Sollich, Peter

doi:10.1103/physrevlett.114.060601

Cited by 127 publications

(233 citation statements)

References 49 publications

(132 reference statements)

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“…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].…”

Section: Introductionmentioning

confidence: 90%

“…(And even for driven systems it is revealing to study the dynamical phase behavior in terms of both empirical currents and activities; see e.g. [33,36,40,45]. )…”

Section: Discussionmentioning

confidence: 99%

“…While empirical currents are the natural trajectory observables to consider in driven problems [1][2][3][4][5]29,30,33,35,36,40], counting observables such as the dynamical activity are central quantities for systems with complex equilibrium dynamics, such as glass formers [24,25,42,43,46]. (And even for driven systems it is revealing to study the dynamical phase behavior in terms of both empirical currents and activities; see e.g.…”

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

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

2017

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Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

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Section: Introductionmentioning

confidence: 90%

“…(And even for driven systems it is revealing to study the dynamical phase behavior in terms of both empirical currents and activities; see e.g. [33,36,40,45]. )…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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

2017

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“…(40), the mapping between the conditioned and driven process is trivial. The driven process is obtained simply by normalising the cMPS, which amounts to shifting the escape rate R by the scaled cumulant generating function θ(s) = γ (e −s − 1), cf.…”

Section: A Examplementioning

confidence: 99%

Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles

Garrahan¹

2016

J. Stat. Mech.

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Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach "biased" or "conditioned" ensembles where the probability of trajectories is biased from that of the natural dynamics by some condition on trajectory observables. In particular, we show that the generalised Doob transform which maps a conditioned process to an equivalent "auxiliary" or "driven" process (one where the same conditioned set of trajectories is generated by a proper stochastic dynamics) is just a gauge transformation of the corresponding cMPS. We also discuss how within this framework one can easily prove properties of the dynamics such as trajectory ensemble equivalence and fluctuation theorems.

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“…On the other hand, (23) means that trajectory PTX has J τ (PTX) = J and (18) implies that dP (PTX) = dP (X). Hence, using (26), one has…”

Section: Ensembles and Pt-symmetrymentioning

confidence: 99%

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Jack

Kaiser

Zimmer

2017

Entropy

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Abstract:We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and driven out of equilibrium by non-conservative forces. We focus on the probabilities of rare events (large deviations). First, we discuss a PT (parity-time) symmetry that appears in ensembles of trajectories where a current is constrained to have a large (non-typical) value. We analyse the heat flow in such ensembles, and compare it with non-equilibrium steady states. Second, we consider pathwise large deviations that are defined by considering many copies of a system. We show how the probability currents in such systems can be decomposed into orthogonal contributions that are related to convergence to equilibrium and to dissipation. We discuss the implications of these results for modelling non-equilibrium steady states.

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Hyperuniformity and Phase Separation in Biased Ensembles of Trajectories for Diffusive Systems

Cited by 127 publications

References 49 publications

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

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

Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

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