A fluctuation theorem for currents and non-linear response coefficients

Andrieux, David; Gaspard, Pierre

doi:10.1088/1742-5468/2007/02/p02006

Cited by 157 publications

(287 citation statements)

References 25 publications

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“…They further predict that in fact the linear response matrix is proportional to the identity, so ) and the set of relations continues to arbitrary high orders. In this way hierarchies [15][16][17], which derive from microreversibility as reflected in the IFR, provide deep insights into nonlinear response theory for nonequilibrium systems (28).…”

Section: Resultsmentioning

confidence: 99%

Symmetries in fluctuations far from equilibrium

Hurtado

Pérez‐Espigares

Pozo

et al. 2011

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

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: Resultsmentioning

confidence: 99%

Symmetries in fluctuations far from equilibrium

Hurtado

Pérez‐Espigares

Pozo

et al. 2011

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

144

View full text Add to dashboard Cite

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“…On the technical level, we build on the recent derivation of a general fluctuation-dissipation theorem for NESSs [3][4][5][6]. By directly working in the NESS, our approach is complementary to work that invokes the fluctuation theorem for deriving non-linear response coefficients in higher order expansions around equilibrium [7,8]. Moreover, it goes beyond similar relations obtained for genuine diffusive spatial transport [9,10] since we require no Euclidean metric and hence the notion of a locally co-moving frame is not available.…”

Section: Institut Für Theoretische Physik Universität Stuttgartmentioning

confidence: 99%

Generalized Einstein or Green-Kubo Relations for Active Biomolecular Transport

Seifert

2010

Phys. Rev. Lett.

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For driven Markovian dynamics on a network of (biomolecular) states, the generalized mobilities, i.e., the response of any current to changes in an external parameter, are expressed by an integral over an appropriate current-current correlation function and thus related to the generalized diffusion constants. As only input, a local detailed balance condition is required typically even valid for biomolecular systems operating deep in the non-equilibrium regime.

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“…The Hamiltonian does not contain the magnetic field and has the symmetry of eq. (12). We denote the whole phase space by S. S is S = S s c ×S s…”

Section: Preparationmentioning

confidence: 99%

“…This idea is originally due to Gallavotti [4]. Gallavotti's idea was applied to the master equation by Andrieux and Gaspard [11,12] to give the non-linear response. In this section, we evaluate the linear response and non-linear response in the current for the case of the McLennan-Zubarev steady distribution.…”

Section: Nonlinear Responsementioning

confidence: 99%

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The McLennan–Zubarev steady state distribution and fluctuation theorems

Sano

2017

Physica A: Statistical Mechanics and its Applications

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The McLennan-Zubarev steady state distribution is studied in the connection with fluctuation theorems. We derive the McLennan-Zubarev steady state distribution from the nonequilibrium detailed balance relation. Then, considering the cumulant function or cumulant functional, two fluctuation theorems for entropy and for currents are proved. Using the fluctuation theorem for currents, the current is expanded in terms of thermodynamic forces. In the lowest order of the thermodynamic force, we find that the transport coefficient satisfies the Onsager's reciprocal relation. In the next order, we derived the correction term to the Green-Kubo formula.

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A fluctuation theorem for currents and non-linear response coefficients

Cited by 157 publications

References 25 publications

Symmetries in fluctuations far from equilibrium

Symmetries in fluctuations far from equilibrium

Generalized Einstein or Green-Kubo Relations for Active Biomolecular Transport

The McLennan–Zubarev steady state distribution and fluctuation theorems

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