Equilibrium States With Macroscopic Correlations

Basile, Giada; Jona-Lasinio, G.

doi:10.1142/s0217979204024094

Cited by 19 publications

(36 citation statements)

References 7 publications

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“…(10) is decoupled from Eq. (9). This decoupling only occurs for non-interacting particles, and it greatly simplifies the problem.…”

Section: Particle Number Statistics and Optimal Pathmentioning

confidence: 99%

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

Meerson¹

2015

J. Stat. Mech.

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Suppose that a point-like steady source at x = 0 injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number N in the steady state is Poisson-distributed with meanN predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given N . We also consider two prototypical examples of interacting diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of N .

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“…(10) is decoupled from Eq. (9). This decoupling only occurs for non-interacting particles, and it greatly simplifies the problem.…”

Section: Particle Number Statistics and Optimal Pathmentioning

confidence: 99%

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

Meerson¹

2015

J. Stat. Mech.

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“…This implies that correlations over macroscopic scales are present. The existence of long range correlations is probably a generic feature of SNS and more generally of situations where the dynamics is not invariant under time reversal [2]. As a consequence if we divide a system into subsystems the free energy is not necessarily simply additive.…”

Section: Thermodynamic Functionals For Non Equilibrium Systemsmentioning

confidence: 99%

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

et al. 2006

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We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional I. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.

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“…for the stationary nonequilibrium state of the zero range process. The microscopic origin of the non-locality of the LDF for the open SEP lies in the O(N −1 ) corrections to LTE which extend over distances of O(N ); N is number of lattice sites, which goes to infinity in the hydrodynamical scaling limit [1,24]. So while the deviations from LTE vanish in this limit their contributions to the LDF, which involves summations over regions of size N , does not…”

Section: Introductionmentioning

confidence: 99%

Large Deviations for a Stochastic Model of Heat Flow

2005

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We investigate a one dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ − and τ + . Kipnis, Marchioro, and Presutti [18] proved that this model satisfies Fourier's law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profileθ(u), u ∈ [−1, 1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different fromθ(u). The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general model and find the features common in these two and other models whose S(θ) is known.

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Equilibrium States With Macroscopic Correlations

Abstract: In this paper we show that the equilibrium macroscopic entropy of a generic non reversibleKawasaki+Glauber dynamics is a non local functional of the density. This implies that equilibrium correlations extend to macroscopic distances.

Cited by 19 publications

References 7 publications

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

Large Deviations for a Stochastic Model of Heat Flow

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