Current fluctuations in the weakly asymmetric exclusion process with open boundaries

Gorissen, Mieke; Vanderzande, Carlo

doi:10.1103/physreve.86.051114

Cited by 27 publications

(40 citation statements)

References 34 publications

(63 reference statements)

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“…The time-independent profiles in these cases, from which a suitable perturbation analysis would hint at the form of the time-dependent solution, are far more complex than the trivial homogeneous profiles that appear for periodic systems, difficulting progress along this line. In fact, a recent study [28] has found no evidence of dynamical phase transition in WASEP with open boundaries. In any case, it seems clear that extremely rare events call in general for coherent, self-organized patterns in order to be sustained [29].…”

Section: Discussionmentioning

confidence: 99%

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

2013

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We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time-dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly-correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, that hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large deviation function, but also the critical current threshold, the associated optimal density profiles and the traveling wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.

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Section: Discussionmentioning

confidence: 99%

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

2013

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“…Although (8) is not satisfied for the parameters considered here, we expect that the AP is still valid. Dynamical phase transitions have only been observed for closed systems [22,[36][37][38], not boundary driven ones [30][31][32]. Also, dynamical phase transitions do not occur for currents close to the average current [23].…”

Section: Current Fluctuationsmentioning

confidence: 99%

“…Under certain conditions, the asymptotic current distribution of a one-dimensional system that is described by the MFT can be calculated from an additivity principle (AP) postulated by Bodineau and Derrida [25]. The validity of this AP has been confirmed in several one-dimensional systems, both analytically [25][26][27][28][29] and numerically [2,[29][30][31][32]. An interesting question is if one can use the AP to predict the current distribution in higher-dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

2015

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We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity principle and the macroscopic fluctuation theory. The current statistics are independent of the shape of the contacts with the reservoirs, provided they are macroscopic in size. In general, the current distribution depends on the spatial dimension. For the special cases of the symmetric simple exclusion process and the zero-range process, the current statistics are the same for all spatial dimensions.

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“…More involved and an open problem as yet, is the stability of the SSEP under an external uniform field E, known as the weakly asymmetric exclusion process (WASEP), which possess the SSEP dynamics given above with a driving field [42]. Since the SSEP is stable for a boundary driven process, so is the WASEP [43]. It is nevertheless worth noting that in the case of periodic boundary conditions, (16) is no longer applicable due to the additional constraint of particle conservation.…”

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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Current fluctuations in the weakly asymmetric exclusion process with open boundaries

Cited by 27 publications

References 34 publications

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

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

Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

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

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