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LCN2 Seminar: Weak and strong ensemble nonequivalence in systems with local constraints

Friday 28 February 2020
Gorlaeus Building
Einsteinweg 55
2333 CC Leiden
Science club

38th LCN2 seminar

Speaker: Qi Zhang

Title: Weak and strong ensemble nonequivalence in systems with local constraints


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 entropies of the two ensembles that is of the same order as the entropies themselves) form. However, recent research on networks has shown that the presence of an extensive number of local constraints can lead to ensemble nonequivalence even in absence of phase transitions. This occurs in a `weak' (i.e. leading to a subleading entropy difference) but remarkably `unrestricted' (i.e. valid in the entire parameter space) form.
Here we look for more general manifestations of ensemble nonequivalence in arbitrary ensembles of matrices with given margins.
These models have widespread applications in the study of spatially heterogeneous and/or temporally non-stationary systems, e.g. gene expression profiles, multi-channel communication systems, multivariate time-series, and bipartite networks.
We confirm that ensemble nonequivalence appears in `unrestricted' form throughout the entire parameter space, due to the extensivity of local constraints. Surprisingly, at the same time, it can also exhibit the `strong' form.
This novel, simultaneously `strong and unrestricted' form of ensemble nonequivalence is very robust and imposes a principled choice of the ensemble in all real-world applications. We calculate the proper mathematical quantities to be used in each case.

About the LCN2 seminar

This talk is part of a series of seminars organized within an ongoing scientific initiative called the "Leiden Complex Networks Network" (LCN2), which brings together scientists with a common interest in both theoretical models and empirical analyses of complex networks and random graphs. The LCN2 community shares the approach of using networks for describing real-world complex systems and aims at developing related analytical and numerical methods, while also being open to other research approaches for studying complex systems. The talks are designed for a broad audience, allowing for constructive exchanges of ideas between scientists from different disciplines. During and after the talk, some drinks and simple snacks are provided.

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