Large deviations of the current in a two-dimensional diffusive system

Pérez‐Espigares, Carlos; Pozo, J. J. del; Garrido, P. L.; Hurtado, Pablo I.

doi:10.1063/1.3569502

Cited by 9 publications

(24 citation statements)

References 2 publications

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“…By using this fluctuating hydrodynamic picture together with a path integral formulation, we derive a general form for the action associated to a history of the density, current and dissipation fields (that is, a path in mesoscopic phase space). Remarkably, this action takes the same form as in conservative nonequilibrium systems [7][8][9][10][11][12][13][14], simplifying the analysis in the dissipative case. This is both an important and a surprising result, which stems from the quasi-elastic character of the underlying microscopic dynamics in the large system size limit.…”

Section: Introductionmentioning

confidence: 99%

“…These intriguing "symmetries" appear as a consequence of the invariance under time reversal of the underlying microscopic dynamics. These and other recent results [5][6][7][8][9][10][11][12][13][14] are however restricted to nonequilibrium "conservative" systems characterized by currents.…”

Section: Introductionmentioning

confidence: 99%

“…This quasi-elasticity is necessary in order to have a balanced competition between diffusion and dissipation at the mesoscopic level. From the derived action functional, and using the recently-introduced additivity conjecture [8,[11][12][13], a general form for the LDF of the dissipated energy is derived, with a "Lagrangian" including second order derivatives. Therefrom, we derive the EulerLagrange equation (a fourth-order differential equation) for the optimal fields responsible of an arbitrary fluctuation.…”

Section: Introductionmentioning

confidence: 99%

“…A classical example is the fluctuation-dissipation theorem, which relates the linear response of a system to an external perturbation to the fluctuation properties of the system in thermal equilibrium [2,3]. More recently, the investigation of general properties of fluctuations in nonequilibrium steady states is opening new paths for understanding physics far from equilibrium [4][5][6][7][8][9][10][11][12][13][14]. The study of fluctuation statistics of macroscopic observables provides an alternative path to obtain thermodynamic potentials, a complementary approach to the usual ensemble description.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, when the colliding pair is chosen completely at random, independently of the value of its energy, the Kipnis-Marchioro-Presutti (KMP) model [23] for heat conduction is recovered in the conservative case. The KMP model plays a main role in nonequilibrium statistical physics as a touchstone to test theoretical advances [5,6,8,[11][12][13][14][15]23]. Our general class of models contains the essential ingredients characterizing most dissipative media, namely: (i) diffusive dynamics, (ii) bulk dissipation, and (iii) boundary injection.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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

102

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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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Thermodynamics of Currents in Nonequilibrium Diffusive Systems: Theory and Simulation

et al. 2013

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Understanding the physics of nonequilibrium systems remains as one of the major challenges of modern theoretical physics. We believe nowadays that this problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics, associated structures and microscopic origin. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new powerful and general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.

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Large deviations of the current in a two-dimensional diffusive system

Cited by 9 publications

References 2 publications

Renormalized time scale for anticipating and lagging synchronization

Renormalized time scale for anticipating and lagging synchronization

Large Deviation Approach to Nonequilibrium Systems

Thermodynamics of Currents in Nonequilibrium Diffusive Systems: Theory and Simulation

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