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The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of…
Consider a topologically exact $C^3$ interval map without non-flat critical points. Following the works we did in \cite{LiRiv12two}, we give two equivalent characterizations of hyperbolic H\"{o}lder continuous potential in terms of the…
The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas…
We discuss a number of illuminating results for tight binding models supporting a band with variable Chern number, and illustrate them explicitly for a simple class of two-banded models. First, for models with a fixed number of bands, we…
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a…
A two-body quantum correlation is calculated for a particle and an infinite potential well in which it is trapped or either a barrier or finite well over which it traverses. Correlated interference results when the incident and reflected…
Information capacities achievable in the multi-parallel-use scenarios are employed to characterize the quantum correlations in unmodulated spin chains. By studying the qubit amplitude damping channel, we calculate the quantum capacity $Q$,…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
We introduce the maximal correlation coefficient $R(M_1,M_2)$ between two noncommutative probability subspaces $M_1$ and $M_2$ and show that the maximal correlation coefficient between the sub-algebras generated by $s_n:=x_1+\ldots +x_n$…
In this work some proposals for black hole entropy interpretation are exposed and investigated. In particular I will firstly consider the so called ``entanglement entropy" interpretation, in the framework of the brick wall model, and the…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
We compute the pair entanglement between two interacting bosons in a two dimensional (2D)isotropic harmonic trap. The interaction potential is modeled by a 2D regularized pseudo-potential. By analytically decomposing the wave function into…
Kahn and Kim (J. Comput. Sci., 1995) have shown that for a finite poset $P$, the entropy of the incomparability graph of $P$ (normalized by multiplying by the order of $P$) and the base-$2$ logarithm of the number of linear extensions of…
We investigate the entanglement and the R\'enyi entropies of two electronic leads connected by a quantum point contact. For non-interacting electrons, the entropies can be related to the cumulants of the full counting statistics of…
Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…
We investigate the entanglement entropy (EE) of circular entangling cuts in the 2+1-dimensional quantum Lifshitz model, whose ground state wave function is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose weight is…
We derive exact and closed-form expressions for a large class of two-point and three-point inflation correlators with the tree-level exchange of a single massive particle. The intermediate massive particle is allowed to have arbitrary mass,…