Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current

In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the observable, that we study through a biased dynamics in a largedeviation framework. We determine explicitly the effective probability-conserving dynamics which makes rare trajectories of the original dynamics become typical trajectories of the effective one. Our approach makes use of a weak-noise path-integral description in which the action is minimised by the rare trajectories of interest. For 'current-type' additive observables, we find the emergence of a propagative trajectory minimising the action for large enough deviations, revealing the existence of a dynamical phase transition at a fluctuating level. In addition, we provide a new method to determine the scaled cumulant generating function of the observable without having to optimise the action. It allows one to show that the weak-noise and the large-time limits commute in this problem. Finally, we show how the biased dynamics can be mapped in practice to an effective driven dynamics, which takes the form of a driven Langevin dynamics in an effective potential. The non-trivial shape of this effective potential is key to understand the link between the dynamical phase transition in the large deviations of current and the standard depinning transition of a particle in a tilted potential. ‡ During the preparation of this manuscript, we became aware that works parallel to ours were completed using similar approaches [22,23].

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“…3. In a periodic system,Ũ (x) is a periodic function of period 1, so that 60) and (63). Following the same reasoning as the one that leads to Eq.…”

Section: Effective Dynamics In the Weak-noise Limitmentioning

confidence: 94%

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Tizón-Escamilla¹,

Lecomte²,

Bertin³

2019

J. Stat. Mech.

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“…This process is physically important as it describes, by means of a modified stochastic process, how fluctuations of the current or any time-integrated observable in general are created in time [23][24][25][26][27][28]. This effective description of fluctuations was illustrated recently in the context of interacting particle systems [29][30][31][32][33], diffusions [34][35][36], and quantum systems [37][38][39][40][41]. For the SDE (1), preliminary results [26] have shown that the auxiliary process modifies not only the driving γ, which is a natural way to increase or decrease the current, but also the potential V (θ) in a non-local and nonlinear way.…”

Section: Introductionmentioning

confidence: 99%

Large deviations of the current for driven periodic diffusions

Nyawo

Touchette

2016

Phys. Rev. E

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We study the large deviations of the time-integrated current for a driven diffusion on the circle, often used as a model of nonequilibrium systems. We obtain the large deviation functions describing the current fluctuations using a Fourier-Bloch decomposition of the so-called tilted generator and also construct from this decomposition the effective (biased, auxiliary or driven) Markov process describing the diffusion as current fluctuations are observed in time. This effective process provides a clear physical explanation of the various fluctuation regimes observed. It is used here to obtain an upper bound on the current large deviation function, which we compare to a recently-derived entropic bound, and to study the low-noise limit of large deviations.

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“…It is worth mentioning that if the constraints obtained are applied on zero-range process with open boundary and local current between left reservoir and the first site, as studied in paper [8], the above constraints reduce to those in [8]. it means that [8] is a special case of our calculations.…”

Section: Effective Generator With Site-dependent Interactions In mentioning

confidence: 97%

Effective stochastic generator with site-dependent interactions

Khamehchi

Jafarpour

2017

Journal of Mathematical Physics

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It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these generators can include local interactions. In this paper we investigate this possibility by considering systems of classical particles moving on a onedimensional lattice with open boundaries. The particles might have hard-core interactions similar to the particles in an exclusion process or there can be arbitrary many particles at single site as in a zero-range process. Assuming that the interactions in the original process are local and site-independent, we will show that under certain constraints on the microscopic reaction rules, the stochastic generator of unconditioned process can be local but site-dependent.As two examples, the asymmetric zero-temperature Glauber model and the A-model with diffusion are presented and studied under the above mentioned constraints.

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Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current

Cited by 58 publications

References 41 publications

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Large deviations of the current for driven periodic diffusions

Effective stochastic generator with site-dependent interactions

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