Microscopic fluctuation theory (mFT) for interacting Poisson processes

Monthus, Cécile

doi:10.1088/1751-8121/ab0978

Cited by 33 publications

(63 citation statements)

References 48 publications

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“…In that respect, the large volume limit of chemical reaction networks is a natural nonlinear version of Markov jump processes, in the same way that interacting diffusions, as described by the macroscopic fluctuation theory [1], are a natural nonlinear version of Fokker-Planck equations. It was brought to our attention that a similar result can be found in [37] in a case where the transitions are limited to the exchange of a single particle. The standard Lagrangian can then be obtained through the contraction formula…”

Section: Detailed Lagrangiansupporting

confidence: 66%

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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Section: Detailed Lagrangiansupporting

confidence: 66%

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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“…An important property of this form of the rate function is that the ratio of the probabilities to observe the empirical currents j r (C , C) and to observe the opposite empirical currents (−j r (C , C)) that would characterize the Backwards trajectories (Eq 18) simplifies into a linear term with respect to the currents in the exponential for any empirical density ρ(C) and activities a r (C , C) Again this is a very direct generalization in the presence of several reservoirs r of the asymmetry with respect to the empirical currents [8,43] : one recognizes the contribution of the action asymmetry (Eq. 37) and the contribution of the entropy asymmetry (Eq.…”

Section: B Joint Probability Of the Empirical Density Empirical Actmentioning

confidence: 98%

“…Again Eq 62 is a very direct generalization in the presence of several reservoirs r of the known formula for Markov jump processes [8,42,43]. Eq.…”

Section: B Joint Probability Of the Empirical Density Empirical Actmentioning

confidence: 99%

Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs

Monthus¹

2019

J. Phys. A: Math. Theor.

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For a system in contact with several reservoirs r at different inverse-temperatures βr, we describe how the Markov jump dynamics with the generalized detailed balance condition can be analyzed via a statistical physics approach of dynamical trajectories [C(t)] 0≤t≤T over a long time interval T → +∞. The relevant intensive variables are the time-empirical density ρ(C), that measures the fractions of time spent in the various configurations C, and the time-empirical jump densities kr(C , C), that measure the frequencies of jumps from configuration C to configuration C when it is the reservoir r that furnishes or absorbs the corresponding energy difference (E(C ) − E(C)). I.arXiv:1906.03606v1 [cond-mat.stat-mech]

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“…with rate functional [27]. See also [7] for a similar rate functional obtained in the framework of time periodic Markov chains and Appendix A for the outline of a simple derivation in the case of independent particles using a Sanov Theorem for paths.…”

Section: Theorem 24 ([29]) the Random Pathsmentioning

confidence: 99%

Dynamical Phase Transitions for Flows on Finite Graphs

Gabrielli

Renger

2020

J Stat Phys

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We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.

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Microscopic fluctuation theory (mFT) for interacting Poisson processes

Cited by 33 publications

References 48 publications

Large deviations and dynamical phase transitions in stochastic chemical networks

Large deviations and dynamical phase transitions in stochastic chemical networks

Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs

Dynamical Phase Transitions for Flows on Finite Graphs

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