Multicanonical distribution: Statistical equilibrium of multiscale systems

Salazar, Domingos S. P.; Vasconcelos, Giovani L.

doi:10.1103/physreve.86.050103

Cited by 9 publications

(17 citation statements)

References 30 publications

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“…Here we assume that ε is a fluctuating quantity but one that varies more slowly (in time and space) than x. Physically, the quantity ε can be identified, for example, with the local energy flux in a turbulent flow [13] or as a 'local temperature' in a hierarchical system in thermal equilibrium [14]. If we sample the system at short intervals but over a long time span (comparable to τ 0 ), then the statistics of x will be described by the marginal distribution…”

Section: The Multiscale Approachmentioning

confidence: 99%

“…Another important ingredient is that we seek a theory that incorporates multiple time scales-a common feature of complex systems-and that clearly exhibits the connection between the local equilibrium variable ε and its large scale counterpart ε 0 . To this end, the Salazar-Vasconcelos model [13,14] recently introduced to describe intermittency in multiscale fluctuation phenonema is a natural starting point. Our approach is also akin in spirit to the Palmer-Stein-Abrahams-Anderson (PSAA) hierarchical model for relaxation in spin glass [15].…”

Section: The Multiscale Approachmentioning

confidence: 99%

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Universality classes of fluctuation dynamics in hierarchical complex systems

et al. 2017

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A unified approach is proposed to describe the statistics of the short time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G-functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

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Section: The Multiscale Approachmentioning

confidence: 99%

Section: The Multiscale Approachmentioning

confidence: 99%

Universality classes of fluctuation dynamics in hierarchical complex systems

et al. 2017

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“…Experimental and theoretical studies on homogeneous and isotropic turbulent flows indicate [5,7,8,10,22,23,26] that the conditional distribution P (δv r | ) is given by a Gaussian with variance . For the sake of simplicity, a Gaussian with zero mean is often considered in theoretical turbulence models [5,13,14,21,25], leading to symmetric (i.e., non-skewed) distributions P (δv r ).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

Sosa-Correa

Pereira²,

Macêdo³

et al. 2019

Phys. Rev. Fluids

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Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and vortex stretching, the form of the asymmetric heavy tails remain elusive. Here we describe the emergence of both properties through an exactly solvable stochastic model with a scale hierarchy of energy transfer rates. From a statistical superposition of a local equilibrium distribution weighted by a background density, the increments distribution is given by a novel class of skewed heavy-tailed distributions, written as a generalization of the Meijer G-functions. Excellent agreement in the multiscale scenario is found with numerical data of systems with different sizes and Reynolds numbers. Remarkably, the single scale limit provides poor fits to the background density, highlighting the central role of the multiscale mechanism. Our framework can be also applied to describe the challenging emergence of skewed distributions in complex systems. arXiv:1812.03199v2 [physics.flu-dyn]

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“…[17,18]. In our approach the system is considered to be effectively composed of a small subsystem in thermal equilibrium with a hierarchical set of heat reservoirs, whose local temperatures fluctuate owing to weak interactions between adjacent reservoirs.…”

Section: B the Distribution Of Statesmentioning

confidence: 99%

“…Here two classes of signal distributions are found [18] according to the behavior at the tails: i) power-law decay and ii) stretched-exponential tail. Applications of the H-theory to empirical data from several systems, such as turbulence [16,17], financial markets [18], and random fiber lasers [20] have yielded excellent results. The dynamical formulation of the H-theory reviewed in the preceding paragraph represents a 'microscopic' (i.e., small-scale) approach to the problem, in that it tries to model the fluctuations in the environment under which the system evolves by a set of stochastic differential equations, which in principle provides a full description of the time-dependent stationary joint distribution function of the background variables.…”

Section: Introductionmentioning

confidence: 99%

Maximum entropy approach toH-theory: Statistical mechanics of hierarchical systems

2018

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A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem-representing the region where the measurements are made-in contact with a set of 'nested heat reservoirs' corresponding to the hierarchical structure of the system. The probability distribution function (pdf) of the fluctuating temperatures at each reservoir, conditioned on the temperature of the reservoir above it, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H-functions. The distribution of states of the small subsystem is then computed by averaging the quasi-equilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H-functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017)] from a stochastic dynamical approach to the problem.

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Multicanonical distribution: Statistical equilibrium of multiscale systems

Cited by 9 publications

References 30 publications

Universality classes of fluctuation dynamics in hierarchical complex systems

Universality classes of fluctuation dynamics in hierarchical complex systems

Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

Maximum entropy approach toH-theory: Statistical mechanics of hierarchical systems

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