Uniform treatment of fluctuations at critical points

Mangel, Marc

doi:10.1016/0378-4371(79)90099-2

Cited by 12 publications

(3 citation statements)

References 23 publications

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“…It is well-known 16 ).17) that no fluctuation diverges in the stationary state for E * O. Therefore our general criterion concludes that there is no slowing down for E *0 in the non-multiplicative stochastic process (2·22).…”

Section: (B) a New Model (To Be Referred To As Sks-model)mentioning

confidence: 55%

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Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes

Suzuki

Kaneko

Sasagawa

1981

Progress of Theoretical Physics

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A general criterion of appearance of slowing down in non·equilibrium stochastic processes is proposed. Many examples for this general criterion are shown, in which a phenomenon of slowing down occurs at a certain value of the relevant parameter. In particular, a generalized scaling treatment of transient phenomena is effectively applied to deriving the relaxation spectra of some multiplicative stochastic processes. The concept of asymptotic slowing down for finite systems is also proposed.

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Section: (B) a New Model (To Be Referred To As Sks-model)mentioning

confidence: 55%

“…The following model can be solved formally: (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) This can be derived, for example, as a model of an autocatalytic reaction, i.e., A + X-=B+ mX. If B is fluctuating around the average, then we obtain the model (2·17).…”

Section: (B) a New Model (To Be Referred To As Sks-model)mentioning

confidence: 99%

Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes

Suzuki

Kaneko

Sasagawa

1981

Progress of Theoretical Physics

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“…Large deviations for normal forms corresponding to codimension-one and codimension-two bifurcations were discussed in a series of papers in the '70s and '80s. We refer to [64,27,28,57,44] and to the review [80] for a detailed analysis. Here we want only to remark that the critical exponent in this framework is equal to that of the mean-field theory.…”

Section: Codimension-one Bifurcations: the Critical Exponentmentioning

confidence: 99%

Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example

2016

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In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory [32]. In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory [6], which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to 1/ √ N , where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter λ, starting from a known quasi-potential for λ = 0. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner [18,19]. Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators [74]. This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively. arXiv:1509.03273v2 [cond-mat.stat-mech]

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Addendum: Description and some aspects of control of temperature fluctuations in catalytic wires and gauzes

Mangel

1981

Mathematical Modelling

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Uniform treatment of fluctuations at critical points

Cited by 12 publications

References 23 publications

Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes

Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes

Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example

Addendum: Description and some aspects of control of temperature fluctuations in catalytic wires and gauzes

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