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

doi:10.1023/a:1014525911391

Cited by 351 publications

(362 citation statements)

References 23 publications

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“…After this paper was submitted for publication, the authors learned of previous related work by Bertini et al 57 Although they did not consider transport statistics, they did consider the probability to manifest a given macroscopic fluctuation of the particle density in diffusive lattice gas models and arrive at the action Eq. (33).…”

Section: Discussionmentioning

confidence: 99%

Fluctuation statistics in networks: A stochastic path integral approach

Jordan

Sukhorukov

Pilgram

2004

Journal of Mathematical Physics

102

185

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The modified optimal path method and non-adiabatic II-order transitions in noisy perturbed dynamical systems AIP Conf. Proc. 502, 54 (2000) We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time evolution of the probability distribution of charges in the network. The building blocks of our theoretical approach are (1) known probability distributions for the connector currents, (2) physical constraints such as local charge conservation, and (3) a time scale separation between the slow charge dynamics of the nodes and the fast current fluctuations of the connectors. We integrate out fast current fluctuations and derive a stochastic path integral representation of the evolution operator for the slow charges. The statistics of charge fluctuations may be found from the saddlepoint approximation of the action. Once the probability distributions on the discrete network have been studied, the continuum limit is taken to obtain a statistical field theory. We find a correspondence between the diffusive field theory and a Langevin equation with Gaussian noise sources, leading nevertheless to nontrivial fluctuation statistics. To complete our theory, we demonstrate that the cascade diagrammatics, recently introduced by Nagaev, naturally follows from the stochastic path integral. By generalizing the principle of minimal correlations, we extend the diagrammatics to calculate current correlation functions for an arbitrary network. One primary application of this formalism is that of full counting statistics (FCS), the motivation for why it was developed in the first place. We stress however, that the formalism is suitable for general classical stochastic problems as an alternative approach to the traditional master equation or Doi-Peliti technique. The formalism is illustrated with several examples: Both instantaneous and time averaged charge fluctuation statistics in a mesoscopic chaotic cavity, as well as the FCS and new results for a generalized diffusive wire.

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Section: Discussionmentioning

confidence: 99%

Fluctuation statistics in networks: A stochastic path integral approach

Jordan

Sukhorukov

Pilgram

2004

Journal of Mathematical Physics

102

185

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“…For equilibrium states it can be shown [4] that V coincides, apart an affine transformation, with the free energy functional (5). Moreover, as shown in [1], the functional V solves the stationary Hamilton-Jacobi equation…”

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confidence: 87%

“…We thus consider an open system in contact with boundary reservoirs, characterized by their chemical potential λ, and under the action of an external field E. We denote by Λ ⊂ R d the bounded region occupied by the system, by x the macroscopic space coordinates and by t the macroscopic time. With respect to our previous work [1,3,4], we here consider the case in which λ and E depend explicitly on the time t, driving the system from a nonequilibrium state to another one. The macroscopic dynamics is given by the hydrodynamic equation for the density which satisfies the following general assumptions based on the notion of local equilibrium.…”

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confidence: 99%

“…Consider a system with time independent driving and let (û(t),(t)), t ∈ [T 1 , T 2 ] be a pair density-current satisfying the continuity equation ∂ tû + ∇ · = 0. According to the basic principles of the macroscopic fluctuation theory [1,3,4], the probability of observing this path is given, up to a prefactor, by exp − ε −d β I [T1,T2] (û,) where ε is the scaling parameter, i.e., the ratio between the microscopic length scale (say the typical intermolecular distance) and the macroscopic one, β = 1/κT (here T is the temperature and κ is Boltzmann's constant), and the action functional I has the form…”

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confidence: 99%

“…From an operational point of view, the quasi potential, a generically nonlocal quantity, can be obtained from the measurement of the density correlation functions. In fact V is the Legendre transform of the generating functional of density correlation functions [1]. On the other hand, the identity W ren = ∆F , that is achieved for quasi static transformations, requires the knowledge of the total current in the intermediate stationary states that can be directly measured.…”

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confidence: 99%

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Clausius Inequality and Optimality of Quasistatic Transformations for Nonequilibrium Stationary States

et al. 2013

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Nonequilibrium stationary states of thermodynamic systems dissipate a positive amount of energy per unit of time. If we consider transformations of such states that are realized by letting the driving depend on time, the amount of energy dissipated in an unbounded time window becomes then infinite. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work performed along any given transformation. We then show that the renormalized work satisfies a Clausius inequality and prove that equality is achieved for very slow transformations, that is in the quasi static limit. We finally connect the renormalized work to the quasi potential of the macroscopic fluctuation theory, that gives the probability of fluctuations in the stationary nonequilibrium ensemble. A main goal of nonequilibrium thermodynamics is to construct analogues of thermodynamic potentials for nonequilibrium stationary states. These potentials should describe the typical macroscopic behavior of the system as well as the asymptotic probability of fluctuations. As it has been shown in [1], this program can be implemented without the explicit knowledge of the stationary ensemble and requires as input the macroscopic dynamical behavior of systems which can be characterized by the transport coefficients. This theory, now known as macroscopic fluctuation theory, is based on an extension of Einstein equilibrium fluctuation theory to stationary nonequilibrium states combined with a dynamical point of view. It has been very powerful in studying concrete microscopic models but can be used also as a phenomenological theory. It has led to several new interesting predictions [2][3][4][5][6][7].From a thermodynamic viewpoint, the analysis of transformations from one state to another one is most relevant. This issue has been addressed by several authors in different contexts. For instance, following the basic papers [8][9][10], the case of Hamiltonian systems with finitely many degrees of freedom has been recently discussed in [11,12] while the case of Langevin dynamics is considered in [13].We here consider thermodynamic transformations for driven diffusive systems in the framework of the macroscopic fluctuation theory. With respect to the authors mentioned above, the main difference is that we deal with systems with infinitely many degrees of freedom and the spatial structure becomes relevant. For simplicity of notation, we restrict to the case of a single conservation law, e.g., the conservation of the mass. We thus consider an open system in contact with boundary reservoirs, characterized by their chemical potential λ, and under the action of an external field E. We denote by Λ ⊂ R d the bounded region occupied by the system, by x the macroscopic space coordinates and by t the macroscopic time. With respect to our previous work [1, 3, 4], we here consider the case in which λ and E depend explicitly on the time t, driving the system from a nonequilibrium state to...

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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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Cited by 351 publications

References 23 publications

Fluctuation statistics in networks: A stochastic path integral approach

Fluctuation statistics in networks: A stochastic path integral approach

Clausius Inequality and Optimality of Quasistatic Transformations for Nonequilibrium Stationary States

Large Deviation Approach to Nonequilibrium Systems

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