Dynamical criticality in open systems: Nonperturbative physics, microscopic origin, and direct observation

Pérez‐Espigares, Carlos; Carollo, Federico; Garrahan, Juan P.; Hurtado, Pablo I.

doi:10.1103/physreve.98.060102

Cited by 13 publications

(25 citation statements)

References 85 publications

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“…Instead of taking a limit where the system size goes to infinity, we utilize a recently introduced formalism [62] where N , the maximum number of particles in the box, is arbitrarily large. Applying the saddle-point method, it is shown that even such models can exhibit DPTs induced by the breaking of the particle-hole symmetry, which was theoretically predicted [44,45] and numerically observed [63] in extended systems, with exactly the same critical exponents. Importantly, the reduced dimensionality of a single-box model allows us to easily predict and confirm the effects of finite time, T , and finite size, N , on the critical phenomena near a symmetrybreaking DPT for arbitrary hopping rates.…”

Section: Introductionmentioning

confidence: 71%

“…which is identical to (63). It is straightforward to show that other choices of dominating terms in Eq.…”

Section: Derivation Of the Scaling Theorymentioning

confidence: 86%

“…These derivations fully justify the scaling behaviors stated in Eqs. (62), (63), and (64). Since the Landau-theory approach we have followed is rather general, we expect that similar behaviors will be observed not only in the DPTs of the single-box SAP, but in the broader range of the generic symmetry-breaking DPTs described in Sec.…”

Section: Derivation Of the Scaling Theorymentioning

confidence: 99%

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Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

Baek¹,

Kafri²,

Lecomte³

2019

J. Stat. Mech.

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We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity large deviation functions of the models can exhibit symmetry-breaking dynamical phase transitions. We characterize exactly the critical properties of these transitions, showing them to be direct analogues of previously studied phase transitions in extended systems. The simplicity of the model allows us to study features of dynamical phase transitions which are not readily accessible for extended systems.In particular, we quantify finite-size and finite-time scaling exponents using both numerical and theoretical arguments. Importantly, we identify an analogue of critical slowing near symmetry breaking transitions and suggest how this can be used in the numerical studies of large deviations. All of our results are also expected to hold for extended systems. CONTENTS

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Section: Introductionmentioning

confidence: 71%

“…which is identical to (63). It is straightforward to show that other choices of dominating terms in Eq.…”

Section: Derivation Of the Scaling Theorymentioning

confidence: 86%

Section: Derivation Of the Scaling Theorymentioning

confidence: 99%

See 1 more Smart Citation

Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

Baek¹,

Kafri²,

Lecomte³

2019

J. Stat. Mech.

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“…This singular change can be rationalized as a second-order DPT where timetranslation symmetry is broken [3,4,6,16,22,26]. Similarly, systems with particle-hole symmetry may exhibit regimes of current fluctuations where the dominant trajectory (or dynamical ground state as termed in the introduction) breaks such particle-hole invariance [38,44,47].…”

Section: The Statistical Physics Of Trajectoriesmentioning

confidence: 97%

“…Additionally, its microscopic origin is not understood yet and, most importantly, such a DPT has never been observed in numerical experiments, which might offer clues on novel phenomenology far from the critical point not yet explored. To shed light on all these issues, we have thoroughly studied the open 1d WASEP using both MFT and cloning Monte Carlo simulations in search of this elusive DPT [47].…”

Section: Particle-hole Symmetry Breaking At the Fluctuation Levelmentioning

confidence: 99%

Sampling rare events across dynamical phase transitions

Pérez‐Espigares

Hurtado

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence. However, during the last decade advanced computational techniques have been developed to measure rare events in simulations of many-particle systems that allow for the first time the direct observation and characterization of these DPTs.Here we review the application of a particular rare-event simulation technique, based on cloning Monte Carlo methods, to characterize DPTs in paradigmatic stochastic lattice gases. In particular, we describe in detail some tricks and tips of the trade, paying special attention to the measurement of order parameters capturing the physics of the different DPTs, as well as to the finite-size effects (both in the system size and number of clones) that affect the measurements. Overall, we provide a consistent picture of the phenomenology associated with DPTs and their measurement. arXiv:1902.01276v2 [cond-mat.stat-mech]

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Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity

Vroylandt

Verley

2018

J Stat Phys

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Dynamical ensembles have been introduced to study constrained stochastic processes. In the microcanonical ensemble, the value of a dynamical observable is constrained to a given value. In the canonical ensemble a bias is introduced in the process to move the mean value of this observable. The equivalence between the two ensembles means that calculations in one or the other ensemble lead to the same result. In this paper, we study the physical conditions associated with ensemble equivalence and the consequences of non-equivalence. For continuous time Markov jump processes, we show that ergodicity guarantees ensemble equivalence. For non-ergodic systems or systems with emergent ergodicity breaking, we adapt a method developed for equilibrium ensembles to compute asymptotic probabilities while caring about the initial condition. We illustrate our results on the infinite range Ising model by characterizing the fluctuations of magnetization and activity. We discuss the emergence of non ergodicity by showing that the initial condition can only be forgotten after a time that scales exponentially with the number of spins.

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Dynamical criticality in open systems: Nonperturbative physics, microscopic origin, and direct observation

Cited by 13 publications

References 85 publications

Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

Sampling rare events across dynamical phase transitions

Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity

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