Large deviations of the empirical current in interacting particle systems

Bertini, Lorenzo; Gabrielli, Davide; Jona-Lasinio, G.; Landim, Cláudio; Sole, Alberto De

doi:10.4213/tvp152

Cited by 34 publications

(83 citation statements)

References 12 publications

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“…How those will manifest themselves in physical or numerical experiments is at this stage an open question. We note that those phase transitions are of different kind than the ones found in [1,2,4,7]. In those works, they are obtained from a quadratic φ when optimizing the energy profile to get a given current.…”

Section: Discussionmentioning

confidence: 99%

“…The theoretical models we will consider are easy to study numerically and well described by a local equilibrium assumption [14,15] in a weakly interacting regime. Using a stochastic approximation, we show that the function describing the macroscopic fluctuations of those models is drastically different from the one generally expected and obtained since the work of Onsager and Machlup [1,2,3,4,5,6,7,23]. As a function of the current it is not a quadratic function around the stationary current.…”

Section: Introductionmentioning

confidence: 92%

See 1 more Smart Citation

Macroscopic fluctuation theory of aerogel dynamics

Lefevere¹,

Mariani²,

Zambotti³

2010

J. Stat. Mech.

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Abstract. We consider the thermodynamic potential describing the macroscopic fluctuation of the current and local energy of a general class of Hamiltonian models including aerogels. We argue that this potential is neither analytic nor strictly convex, a property that should be expected in general but missing from models studied in the literature. This opens the possibility of describing in terms of a thermodynamic potential non-equilibrium phase transitions in a concrete physical context. This special behaviour of the thermodynamic potential is caused by the fact that the energy current is carried by particles which may have arbitrary low speed with sufficiently large probability.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Macroscopic fluctuation theory of aerogel dynamics

Lefevere¹,

Mariani²,

Zambotti³

2010

J. Stat. Mech.

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“…In boundary or field driven systems [8,13,38,39,40,14], for instance, this entropy flow is simply proportional to the particle current flowing through the system, the proportionality constant being the force driving the system out of equilibrium (a chemical potential or a temperature gradient, an applied field, etc.). It is characterized by a nontrivial large deviation function only for nonequilibrium systems (more precisely those breaking detailed balance but for which W (C → C ′ ) = 0 only if W (C ′ → C) = 0).…”

Section: Large Deviation Formalism Time-reversed Ks Entropy and Entmentioning

confidence: 99%

Thermodynamic Formalism for Systems with Markov Dynamics

2007

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The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time.We also generalize the formalism -a dynamical Gibbs ensemble constructionto a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem.We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.

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“…when one considers the total current flowing through the system, the large deviation function derived from the hydrodynamic theory satisfies for large L and J of order 1 a scaling similar to the one dimensional case [4] …”

Section: Introductionmentioning

confidence: 99%

Vortices in the Two-Dimensional Simple Exclusion Process

Bodineau

Derrida²,

Lebowitz

2008

J Stat Phys

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Abstract. We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partial flux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed in an Appendix.

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Large deviations of the empirical current in interacting particle systems

Cited by 34 publications

References 12 publications

Macroscopic fluctuation theory of aerogel dynamics

Macroscopic fluctuation theory of aerogel dynamics

Thermodynamic Formalism for Systems with Markov Dynamics

Vortices in the Two-Dimensional Simple Exclusion Process

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