Related papers: Strong ensemble nonequivalence in systems with loc…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and…
We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures. This is obtained by proving a local central limit theorem and a local large…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
Because the constant extension ensemble of single chain molecule is not always equivalent with constant force ensemble, a model of double-stranded conformations, as in RNA molecules and $\beta$-sheets in proteins, with fixed extension…
We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the…
Neural network potentials (NNPs) combine the computational efficiency of classical interatomic potentials with the high accuracy and flexibility of the ab initio methods used to create the training set, but can also result in unphysical…
The Random Transverse Field Ising Chain is the simplest disordered model presenting a quantum phase transition at T=0. We compare analytically its finite-size scaling properties in two different ensembles for the disorder (i) the canonical…
The use of emergent constraints to quantify uncertainty for key policy relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become increasingly widespread in recent years. Many researchers, however, claim that emergent…
We compare the transition barrier that accompanies a first-order phase transition in the canonical and microcanonical ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a…
In [18] we analysed a simple undirected random graph subject to constraints on the total number of edges and the total number of triangles. We considered the dense regime in which the number of edges per vertex is proportional to the number…
Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators. Here we present a framework to systematically include quantum effects arising from the…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries -- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…
We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schr\"odinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble…