Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity

Vroylandt, Hadrien; Verley, Gatien

doi:10.1007/s10955-018-2186-7

Cited by 11 publications

(9 citation statements)

References 47 publications

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“…Maxwell construction and additivity violation.-A natural question is whether time-dependent optimal trajectories exist which improve the additivity principle minimizers. The emergence of a non-convex regime in G(m|q) for |q| < |q c | suggests a Maxwell-like instantonic solution in this region [26,32,71]. In particular, as we show in [70], for PH-symmetric boundaries, fixed |q| < |q c | and m ∈ (m − q , m + q ), a trajectory which jumps smoothly (in a finite time)…”

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confidence: 53%

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

et al. 2018

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Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the open weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a Z2 symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetrybroken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations, confirming our macroscopic and microscopic results.

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confidence: 53%

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

et al. 2018

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“…Those equations of motion must be verified by the typical trajectories of the system, in particular if we start from a certain concentration ρ 0 and simply trace over the final concentration by taking θ t = 0. Since we have an explicit expression for L, we could inject it in (45), but that is not necessary: we know that L is positive by construction and cancels only at…”

Section: Equations Of Motionmentioning

confidence: 99%

“…The sign of the Hamiltonian is indicated in each region, as a reference for the following deformations, in order to identify the critical point with highest value of H. Note that, in this context, the whole dynamics takes place on the f = 0 line due to the final condition, and that the notion of stability of fixed points is therefore different from the fluctuating case. Also note that the stable fixed point that will be reached depends on the initial condition, which is due to the breaking of ergodicity in the large-volume limit [44,45]. We represent the fixed point with the highest value of the Hamiltonian in green.…”

Section: A Schlögl Modelmentioning

confidence: 99%

Large deviations and dynamical phase transitions in stochastic chemical networks

Lazarescu

Cossetto

Falasco

et al. 2019

The Journal of Chemical Physics

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Chemical reaction networks offer a natural nonlinear generalisation of linear Markov jump processes on a finite state-space. In this paper, we analyse the dynamical large deviations of such models, starting from their microscopic version, the chemical master equation. By taking a largevolume limit, we show that those systems can be described by a path integral formalism over a Lagrangian functional of concentrations and chemical fluxes. This Lagrangian is dual to a Hamiltonian, whose trajectories correspond to the most likely evolution of the system given its boundary conditions.The same can be done for a system biased on time-averaged concentrations and currents, yielding a biased Hamiltonian whose trajectories are optimal paths conditioned on those observables. The appropriate boundary conditions turn out to be mixed, so that, in the long time limit, those trajectories converge to well-defined attractors. We are then able to identify the largest value that the Hamiltonian takes over those attractors with the scaled cumulant generating function of our observables, providing a non-linear equivalent to the well-known Donsker-Varadhan formula for jump processes.On that basis, we prove that chemical reaction networks that are deterministically multistable generically undergo first-order dynamical phase transitions in the vicinity of zero bias. We illustrate that fact through a simple bistable model called the Schlögl model, as well as multistable and unstable generalisations of it, and we make a few surprising observations regarding the stability of deterministic fixed points, and the breaking of ergodicity in the large-volume limit. arXiv:1902.08416v1 [cond-mat.stat-mech]

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“…In addition, by combining Eqs. (87), (89) and (96) with the scaling in (97), we obtain for the correlators of the noise fields in the diffusive scaling limit…”

Section: Hydrodynamic Fluctuationsmentioning

confidence: 99%

The kinetic exclusion process: a tale of two fields

Gutiérrez-Ariza

Hurtado

2019

J. Stat. Mech.

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We introduce a general class of stochastic lattice gas models, and derive their fluctuating hydrodynamics description in the large size limit under a local equilibrium hypothesis. The model consists in energetic particles on a lattice subject to exclusion interactions, which move and collide stochastically with energy-dependent rates. The resulting fluctuating hydrodynamics equations exhibit nonlinear coupled particle and energy transport, including particle currents due to temperature gradients (Soret effect) and energy flow due to concentration gradients (Dufour effect). The microscopic dynamical complexity is condensed in just two matrices of transport coefficients: the diffusivity matrix (or equivalently the Onsager matrix) generalizing Fick-Fourier's law, and the mobility matrix controlling current fluctuations. Both transport coefficients are coupled via a fluctuation-dissipation theorem, suggesting that the noise terms affecting the local currents have Gaussian properties. We further prove the positivity of entropy production in terms of the microscopic dynamics. The so-called kinetic exclusion process has as limiting cases two of the most paradigmatic models of nonequilibrium physics, namely the symmetric simple exclusion process of particle diffusion and the Kipnis-Marchioro-Presutti model of heat flow, making it the ideal testbed where to further develop modern theories of nonequilibrium behavior.

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Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity

Cited by 11 publications

References 47 publications

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

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

Large deviations and dynamical phase transitions in stochastic chemical networks

The kinetic exclusion process: a tale of two fields

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