Related papers: Shadowing, sensitivity and entropy points
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
Chaos thresholds of the $z$-logistic maps $x_{t+1}=1-a|x_t|^z$ $(z>1; t=0,1,2,...)$ are numerically analysed at accumulation points of cycles 2, 3 and 5. We verify that the nonextensive $q$-generalization of a Pesin-like identity is…
Using the idea of local entropy theory, we characterize the sequence entropy tuple via mean forms of the sensitive tuple in both topological and measure-theoretical senses. For the measure-theoretical sense, we show that for an ergodic…
The entanglement entropy in Kondo impurity systems is studied analytically using conformal field theory. From the impurity contribution to the scaling corrections of the entanglement entropy we extract information about the screening cloud…
Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to…
Entropy arises in strong interactions by a dynamical separation of ``partons'' from unobservable ``environment'' modes due to confinement. For interacting scalar fields we calculate the statistical entropy of the observable subsystem.…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network…
For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.
The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we…
A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980's that the only route to positive topological entropy is through a cascade of period…
Holographic studies of the entanglement entropy of field theories dual to charged and neutral black holes in asymptotically global AdS4 spacetimes are presented. The goal is to elucidate various properties of the quantity that are peculiar…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than…
We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is…
We investigate local entropy theory, particularly the property of having completely positive entropy (CPE), from a descriptive set-theoretic point of view. We aim to determine descriptive complexity of different families of dynamical…
Entropy of matter in a very strong gravity depends on cross-sectional area of the container of the system -- is being further bolstered by calculating entropy of a monoatomic gas kept under uniform strong gravity at Newtonian scale. This…
We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface $\Sigma$. We find that this number is proportional to the…