Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles

@article{Ellis2000LargeDP,
  title={Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles},
  author={Richard S. Ellis and Kyle Haven and Bruce Turkington},
  journal={Journal of Statistical Physics},
  year={2000},
  volume={101},
  pages={999-1064}
}
We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and… 

Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows

Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence

ANALYSIS OF STATISTICAL EQUILIBRIUM MODELS OF GEOSTROPHIC TURBULENCE

Statistical equilibrium lattice models of coherent structures in geostrophic turbulence, formulated by discretizing the governing Hamiltonian continuum dynamics, are analyzed. The first set of

Equivalence and Nonequivalence of the Microcanonical and Canonical Ensembles: A Large Deviations Study

3 4 SUMMARY This thesis presents an in-depth study of statistical mechanical systems having microcano-nical equilibrium properties, i.e., energy-dependent equilibrium properties, which cannot be put

Global Optimization, the Gaussian Ensemble, and Universal Ensemble Equivalence.

Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates

Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

AbstractThe gaussian ensemble and its extended version theoretically play the important role of interpolating ensembles between the microcanonical and the canonical ensembles. Here, the thermodynamic

The Generalized Canonical Ensemble and Its Universal Equivalence with the Microcanonical Ensemble

This paper shows for a general class of statistical mechanical models that when the microcanonical and canonical ensembles are nonequivalent on a subset of values of the energy, there often exists a

Equivalence and Nonequivalence of Ensembles: Thermodynamic, Macrostate, and Measure Levels

We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics—namely,

The extended Gaussian ensemble and metastabilities in the Blume?Capel model

The Blume-Capel model with infinite-range interactions presents analytical solutions in both canonical and microcanonical ensembles and therefore, its phase diagram is known in both ensembles. This

Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

Abstract. A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium
...

References

SHOWING 1-10 OF 59 REFERENCES

Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows

Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence

STATISTICAL EQUILIBRIUM MEASURES AND COHERENT STATES IN TWO-DIMENSIONAL TURBULENCE

The equilibrium statistics of the Euler equations in two dimensions are studied, and a new continuum model of coherent, or organized, states is proposed. This model is defined by a maximum entropy

A special class of stationary flows for two-dimensional euler equations: A statistical mechanics description. Part II

We continue and conclude our analysis started in Part I (see [CLMP]) by discussing the microcanonical Gibbs measure associated to a N-vortex system in a bounded domain. We investigate the Mean-Field

Negative-temperature states and large-scale, long-lived vortices in two-dimensional turbulence

We study Onsager's theory of large, coherent vortices in turbulent flows in the approximation of the point-vortex model for two-dimensional Euler hydrodynamics. In the limit of a large number of

Statistical dynamics of two-dimensional flow

  • R. Kraichnan
  • Physics, Environmental Science
    Journal of Fluid Mechanics
  • 1975
The equilibrium statistical mechanics of inviscid two-dimensional flow are re-examined both for a continuum truncated at a top wavenumber and for a system of discrete vortices. In both cases, there

Statistical Mechanics, Euler’s Equation, and Jupiter’s Red Spot

A statistical-mechanical treatment of equilibrium flows in the two-dimensional Euler fluid is constructed which respects all conservation laws. The vorticity field is fundamental, and its long-range

Statistical mechanics, Euler's equation, and Jupiter's Red Spot.

Derivation of Maximum Entropy Principles in Two-Dimensional Turbulence via Large Deviations

The continuum limit of lattice models arising in two-dimensional turbulence is analyzed by means of the theory of large deviations. In particular, the Miller–Robert continuum model of equilibrium

Large Deviations and Maximum Entropy Principle for Interacting Random Fields on $\mathbb{Z}^d$

We present a new approach to the principle of large deviations for the empirical field of a Gibbsian random field on the integer lattice Zd. This approach has two main features. First, we can replace
...