Large Fluctuations in Driven Dissipative Media

Prados, A.; Lasanta, Antonio; Hurtado, Pablo I.

doi:10.1103/physrevlett.107.140601

Cited by 53 publications

(102 citation statements)

References 22 publications

(34 reference statements)

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“…This type of dependence is common to many driven dissipative media, as for instance the general family of models that we will study in section IV [25,39] or different reaction-diffusion systems [43]. However, it should be noted that not all systems obey this homogeneity condition, e.g.…”

Section: A Small Fluctuations Around the Averagementioning

confidence: 99%

“…The physical reason for this behavior is that the microscopic dynamics must be quasi-elastic in order to ensure that dissipation and diffusion take place over the same time scale in the thermodynamic limit. Typically, 1 − α must scale as L −2 that is the order of magnitude of the diffusive term in a system of length L [25,39]. The boundary conditions for eq (2.1) depend on the physical situation of interest.…”

Section: Macroscopic Fluctuation Theory For Driven Dissipative Symentioning

confidence: 99%

“…(2.21), the generalized momentum p λj verifies 25) where p j is the generalized momentum for the Lagrangian L, that is,…”

Section: B Mapping the Constraint To Boundary Conditionsmentioning

confidence: 99%

“…(2.1) at every point of space and time [12]. This probability hence obeys a large deviation principle of the form [4,[7][8][9][10][11][12][13]25]…”

Section: Macroscopic Fluctuation Theory For Driven Dissipative Symentioning

confidence: 99%

“…Section III is devoted to the detailed study of different asymptotic behaviors within the Hamiltonian formulation, which turns out to simplify the analysis. In section IV we define a general class of microscopic lattice models whose stochastic dynamics is dissipative [25,39]. The theoretical framework developed in the previous sections is applied to this family of models in section V, and the LDF for the dissipated energy is explicitly worked out.…”

Section: Introductionmentioning

confidence: 99%

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Renormalized time scale for anticipating and lagging synchronization

2016

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We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated to a path in mesoscopic phase-space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in non-dissipative systems. This is a consequence of the quasi-elasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always gaussian, as expected from the central limit theorem. On the other hand, strong separation from the gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily supressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases non-convex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of describing in detail the fluctuating behavior of nonlinear driven dissipative media.

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Section: A Small Fluctuations Around the Averagementioning

confidence: 99%

Section: Macroscopic Fluctuation Theory For Driven Dissipative Symentioning

confidence: 99%

“…(2.21), the generalized momentum p λj verifies 25) where p j is the generalized momentum for the Lagrangian L, that is,…”

Section: B Mapping the Constraint To Boundary Conditionsmentioning

confidence: 99%

“…(2.1) at every point of space and time [12]. This probability hence obeys a large deviation principle of the form [4,[7][8][9][10][11][12][13]25]…”

Section: Macroscopic Fluctuation Theory For Driven Dissipative Symentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Renormalized time scale for anticipating and lagging synchronization

2016

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Large Deviation Approach to Nonequilibrium Systems

Touchette

Harris

2013

Nonequilibrium Statistical Physics of Small Systems

101

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The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A similar approach has been followed more recently for nonequilibrium systems, especially in the context of interacting particle systems. We review here the basis of this approach, emphasizing the similarities and differences that exist between the application of large deviation theory for studying equilibrium systems on the one hand and nonequilibrium systems on the other. Of particular importance are the notions of macroscopic, hydrodynamic, and long-time limits, which are analogues of the equilibrium thermodynamic limit, and the notion of statistical ensembles which can be generalized to nonequilibrium systems. For the purpose of illustrating our discussion, we focus on applications to Markov processes, in particular to simple random walks.

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Hydrodynamics: A Sea of Grains

Puglisi

2014

SpringerBriefs in Physics

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Large Fluctuations in Driven Dissipative Media

Cited by 53 publications

References 22 publications

Renormalized time scale for anticipating and lagging synchronization

Renormalized time scale for anticipating and lagging synchronization

Large Deviation Approach to Nonequilibrium Systems

Hydrodynamics: A Sea of Grains

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