Related papers: Complexity of two-level systems
The electronic density \rho(r) in atoms, molecules and solids is, in general, a distribution that can be observed experimentally, containing spatial information projected from the total wave function. These density distributions can be…
The Wehrl entropy of a quantum state is the Shannon entropy of its coherent-state distribution function, and remains non-zero even for pure states. We investigate the relationship between this entropy and the many-particle quantum…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We study the information entropy, order, disorder, and complexity for the two-dimensional (2D) rotating and nonrotating Bose-Einstein condensates. The choice of our system is a complete theoretical laboratory where the complexity is…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…
We investigate the entanglement between a spin and its environment in impurity systems which exhibit a second-order quantum phase transition. As an application, we employ the spin-boson model, describing a two-level system (spin) coupled to…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…
The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
Understanding quantum thermalization through entanglement build-up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Here, we study the spin dynamics and approach towards…