Strong ensemble nonequivalence in systems with local constraints

@article{Zhang2022StrongEN,
  title={Strong ensemble nonequivalence in systems with local constraints},
  author={Qi Ren Zhang and Diego Garlaschelli},
  journal={New Journal of Physics},
  year={2022},
  volume={24}
}
The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical applications. However, this property breaks down under certain circumstances. The most studied violation of ensemble equivalence requires phase transitions, in which case it has a ‘restricted’ (i.e. confined to a certain region in parameter space) but ‘strong’ (i.e. characterized by a difference between the… 
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References

SHOWING 1-10 OF 23 REFERENCES

Breaking of Ensemble Equivalence in Networks.

TLDR
It is shown that ensemble nonequivalence can manifest itself also in random graphs with topological constraints, and it is found that, while graphs with a given number of links are ensemble equivalent, graphsWith a given degree sequence are not.

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,

Covariance Structure Behind Breaking of Ensemble Equivalence in Random Graphs

TLDR
This paper analyses a formula for the relative entropy of generic discrete random structures recently put forward by Squartini and Garlaschelli, and shows that in the dense regime this formula correctly predicts that the specific relative entropy is determined by the scaling of the determinant of the matrix of canonical covariances of the constraints.

Ensemble nonequivalence in random graphs with modular structure

Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in

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

Nonequivalence of ensembles for long-range quantum spin systems in optical lattices.

TLDR
The anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions is studied and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters.

The statistical physics of real-world networks

TLDR
This Review describes advances in the statistical physics of complex networks and provides a reference for the state of the art in theoretical network modelling and applications to real-world systems for pattern detection and network reconstruction.

Ensemble equivalence for dense graphs

TLDR
This paper considers a random graph on which topological restrictions are imposed, such as constraints on the total number of edges, wedges, and triangles, and finds that breaking of ensemble equivalence occurs when the constraints are frustrated.