Dynamical phase transition for current statistics in a simple driven diffusive system

Espigares, Carlos Pérez; Garrido, P. L.; Hurtado, Pablo I.

doi:10.1103/physreve.87.032115

Cited by 83 publications

(93 citation statements)

References 46 publications

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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: 82%

“…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%

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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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Section: Introductionmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

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

2017

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“…This condition together with the linear set of equations (17) give a constructive and easy to implement prescription to find the frequency ω 0 and spatial amplitude f ω0 (x) of a time-dependent density mode ρ (x, τ ) = ρ AP (x) + e iω0τ f ω0 (x) + e −iω0τ f * ω0 (x) which minimises the action (12). Similar considerations applied to systems with spatial periodic boundary conditions [23,[36][37][38], lead to a closed expression of such an unstable mode ω 0 . Although a closed expression can hardly be obtained for open systems considered here, the general conclusions seem to hold in that case as well, namely, for finite size L and long time limit t → ∞, the first unstable mode is expected to be the fundamental so that the system is driven through a continuous, second order like transition [23].…”

Section: Pacs Numbersmentioning

confidence: 99%

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

Shpielberg

Akkermans

2016

Phys. Rev. Lett.

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A stability analysis of out of equilibrium and boundary driven systems is presented. It is performed in the framework of the hydrodynamic macroscopic fluctuation theory and assuming the additivity principle whose interpretation is discussed with the help of a Hamiltonian description. An extension of Le Chatelier principle for out of equilibrium situations is presented which allows to formulate the conditions of validity of the additivity principle. Examples of application of these results in the realm of classical and quantum systems are provided. PACS numbers:Understanding the behaviour of out of equilibrium systems is an essential problem in physics [1] but surprisingly enough and except for few exact solutions, it still lacks both a macroscopic approach comparable to thermodynamics and a microscopic theory. However, a fruitful hydrodynamic description of driven diffusive systems far from equilibrium, the macroscopic fluctuation theory (hereafter MFT) has been proposed [2]. It is based on a variational principle which provides equations for the time evolution of the most probable density profile corresponding to a given fluctuation. The MFT was used to explore aspects of out of equilibrium systems [3][4][5][6][7][8]. The case of current fluctuations has been singled out due to its relevance to a broad range of problems generically known as full counting statistics which play an important role both in classical and quantum systems [9][10][11][12][13]. Quite often, a classical description is convenient enough to account for the behaviour of quantum systems driven out of equilibrium. Noise and current statistics in disordered quantum mesoscopic conductors or wave speckles [14,15], non equilibrium spins in superconductors [16] and thermal transport [17,18] provide important examples of such quantum systems. A great amount of effort has been devoted to the investigation of large current fluctuations since they provide a measure of the likeliness of the system to return to equilibrium. Whereas close to equilibrium, energy and density are almost uniform and can be described within linear response theory, for driving currents far enough from the steady state current, the system may preferably choose non uniform and timedependent solutions for these observables, very much like a dynamical phase transition.To make these considerations more precise, we consider a large system of size L connected for a long time to reservoirs of particles at different densities. It reaches a non-equilibrium steady state with a non vanishing and fluctuating particle current. These fluctuations are characterised by the probability P t (Q) for having a number of particles Q flowing through the medium during a time t. In the long time limit t → ∞, this probability follows a large deviation principle,where the large deviation function Φ t plays in that situation a role similar to the equilibrium free energy [19] Expression (1) is not an obvious result [20]. Moreover, finding an explicit expression for Φ t is a difficult optimisation problem. H...

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“…Analysis of fluctuations in non-equilibrium processes have, for example, led to the discovery of the fluctuation theorems, which have helped elucidate how macroscopic notions of irreversibility emerge from microscopic laws [1][2][3]. More recently, theoretical and numerical analysis of the statistics of rare fluctuations in driven lattice gas models [4,5], exclusion processes [6], zero-range processes [7], 1D models of transport [8], and models of glass formers [9,10] have revealed the presence of coexisting ensembles of trajectories and so-called dynamic phase transitions between them [4,5,8,11]. In this paper, we analyze the statistics of rare fluctuations in entropy production rates for certain model non-equilibrium, or driven, kinetic networks (see Fig.…”

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confidence: 99%

Dynamic phase transitions in simple driven kinetic networks

2014

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We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, where energy fluxes typically result in non-equilibrium dynamics. By analyzing the fluctuations in the entropy production, we demonstrate the emergence, in a large system size limit, of a dynamic phase transition between two distinct dynamical regimes.The study of fluctuation phenomena is one of the central endeavors of non-equilibrium statistical mechanics. Analysis of fluctuations in non-equilibrium processes have, for example, led to the discovery of the fluctuation theorems, which have helped elucidate how macroscopic notions of irreversibility emerge from microscopic laws [1][2][3]. More recently, theoretical and numerical analysis of the statistics of rare fluctuations in driven lattice gas models [4,5], exclusion processes [6], zero-range processes [7], 1D models of transport [8], and models of glass formers [9,10] have revealed the presence of coexisting ensembles of trajectories and so-called dynamic phase transitions between them [4,5,8,11]. In this paper, we analyze the statistics of rare fluctuations in entropy production rates for certain model non-equilibrium, or driven, kinetic networks (see Fig. 1). While this Markovian system, with effectively one-particle dynamics, lacks much of the complexity of previously studied driven systems [4-8], we show -numerically and analyticallythe presence of two dynamical phases, each with a characteristic entropy production rate. This demonstration shows that singularities in trajectory space can in fact arise even in very simple driven kinetic networks with a single degree of freedom. Driven kinetic networks of this general flavor are used to model a variety of physical, chemical, and biological systems including molecular motor dynamics [12,13]; cellular feedback, control, and regulation [14]; and kinetic proofreading mechanisms [15,16]. Physically, the dynamic phase transition serves to enhance the probability of observing large fluctuations in the dynamical behavior of these hopping processes.We study dynamical fluctuations of a system evolving on cyclical or periodic driven kinetic networks with some heterogeneity in the transition rates. We consider two types of cyclic networks, which we hereafter refer to as the ring network and the triangle network. The ring network connects N states in a circle with transition rates x in the clockwise direction and 1 in the reverse direction. The network has translational symmetry, but we also construct a variation of the ring network with that symmetry broken by a link we call the heterogeneous link, or h-link. As shown in Fig.

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Dynamical phase transition for current statistics in a simple driven diffusive system

Cited by 83 publications

References 46 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

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

Dynamic phase transitions in simple driven kinetic networks

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