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

Pérez-Espigares, C.; Pozo, J. J. del; Garrido, P. L.; Hurtado, Pablo I.; Garrido, Pedro L.; Marro, Joaquín; Santos, F. de los

doi:10.1063/1.3577629

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“…Fig. 3 shows the measured μðλÞ for different values of jλ þ ϵj corresponding to very large current fluctuations, different rotation angles ϕ and increasing system sizes, together with the theoretical predictions (29). As a result of the finite, discrete character of the lattice system studied here, we observe weak violations of IFR in the far tails of the current distribution, specially for currents orthogonal to ϵ.…”

Section: Checking the Isometric Fluctuation Relationmentioning

confidence: 90%

“…The model is described at the macroscopic level by Eq. 2 with a diffusive current term Q½ρðr;tÞ ¼ −D½ρ∇ ρ with D½ρ ¼ 1 the IFR because: (i) the associated hydrodynamic fluctuation theory can be solved analytically (29), and (ii) its dynamics is simple enough to allow for a detailed numerical study of current fluctuations.…”

Section: Checking the Isometric Fluctuation Relationmentioning

confidence: 99%

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Symmetries in fluctuations far from equilibrium

Hurtado

Pérez‐Espigares

Pozo

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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144

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Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. large deviations | rare events | hydrodynamics | transport | entropy production L arge fluctuations, though rare, play an important role in many fields of science as they crucially determine the fate of a system (1). Examples range from chemical reaction kinetics or the escape of metastable electrons in nanoelectronic devices to conformational changes in proteins, mutations in DNA, and nucleation events in the primordial universe. Remarkably, the statistics of these large fluctuations contains deep information on the physics of the system of interest (2, 3). This is particularly important for systems far from equilibrium, where no general theory exists up to date capable of predicting macroscopic and fluctuating behavior in terms of microscopic physics, in a way similar to equilibrium statistical physics. The consensus is that the study of fluctuations out of equilibrium may open the door to such general theory. As most nonequilibrium systems are characterized by currents of locally conserved observables, understanding current statistics in terms of microscopic dynamics has become one of the main objectives of nonequilibrium statistical physics (2-17). Pursuing this line of research is both of fundamental as well as practical importance. At the theoretical level, the function controlling current fluctuations can be identified as...

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Section: Checking the Isometric Fluctuation Relationmentioning

confidence: 90%

Section: Checking the Isometric Fluctuation Relationmentioning

confidence: 99%