Space-time phase transitions in driven kinetically constrained lattice models

Speck, Thomas; Garrahan, Juan P.

doi:10.1140/epjb/e2010-10800-x

Cited by 26 publications

(31 citation statements)

References 39 publications

(41 reference statements)

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“…(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%

“…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: 99%

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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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“…(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: Introductionmentioning

confidence: 99%

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

2017

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“…Counting processes of the type we consider, unlike 'symmetric' ones, are odd with respect to time reversal. This is related to a Gallavotti-Cohen symmetry [15] due to the driven nature of the systemʼs dynamics [32]. In contrast to most studied examples of systems presenting such dynamical properties, the dynamics of a global, rather than a local, degree of freedo are considered here.…”

Section: K K Kmentioning

confidence: 99%

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

et al. 2015

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We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.Understanding and controlling the dynamical behavior of quantum systems has seen flourishing interest [1][2][3] propelled by theoretical and experimental progress that has made it possible to observe and manipulate such systems with unprecedented accuracy. Much attention has also been devoted recently to the notion of dynamical phase transitions in such systems, relating them to the nonanalyticity of, e.g., the Loschmidt echo [4] or the logarithm of a biased partition function in large-deviation (LD) theory [5], which has a natural interpretation in terms of the statistics of rare trajectories observed in experiments. The study of the dynamics of quantum systems through LD methods [6-8] emerged recently both as an extension of the theory as applied to classical systems [9][10][11][12] and as a dynamical complement to the standard analysis of equilibrium phase transitions in many-body systems [13]. Here, nonanalyticities in the LD free-energy function of a system, extracted from the equations governing its dynamical behavior, are identified in the literature with dynamical phase transition points [6].Following [6], in this paper we are interested in studying the statistical properties of rare quantum-jump trajectories [14] of a system that interacts with a heat bath driving the system out of equilibrium. We consider the dynamical LD properties of a simple three-spin quantum open model, which departs from those recently studied in two respects: first, dissipation is due to nonclassical bilinear jump operators; and second, we consider a current-like dynamical order parameter. The two central results in this paper are (a) the observation of intermittency between dynamical phases of distinct activity, itself a consequence of the reducibility of the dynamics in an appropriate limit due to the collective jump operators; and (b) the existence of a Gallavotti-Cohen symmetry in LD functions associated with the time-asymmetric order parameter, analogous to that found in driven classical systems [15], which gives rise to a fluctuation theorem [16] relating to the quantum jump rate. Our system therefore provides a minimal but extendible model that uncovers the effects of thermal baths and the nontrivial interplay between local and global decay channels [17] on the non-equilibrium dynamics of a quantum system.We start with three spins-1/2, which we label = j 1, 2, 3, placed at ...

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“…Hence, one can study large deviations of two different dynamical quantities of interest, namely the activity K(t) and the integrated current Q(t) = t 0 J(t ′ )dt ′ , defined as the number of moves in the direction of the field between time 0 and t. For a mean-field version of a driven FA model, a first-order transition is found for the entropy production, at s = 0 in [26]. The result seems to be true also for a 2d KCM studied numerically by TPS.…”

Section: Glassy Lattice Models With External Forcingmentioning

confidence: 99%

Large deviations and heterogeneities in driven or non-driven glassy systems

Pitard

2013

EPJ Web of Conferences

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Abstract. We give a short overview of the results for large deviations of dynamical quantities obtained for models of glassy systems. We introduce the paper with the study of kinetically constrained models (KCMs), first without external forcing. In these models, it has been shown using the thermodynamic formalism for histories, that there is a coexistence between an active and an inactive phase. Later, it has been found that adding a driving field to a KCM model leads to a singularity in the large deviation function of the current at large fields. Finally we report on recent studies on realistic glassy systems, and open directions for future research.

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Space-time phase transitions in driven kinetically constrained lattice models

Cited by 26 publications

References 39 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

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

Large deviations and heterogeneities in driven or non-driven glassy systems

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