Related papers: How much information can one store in a non-equili…
In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite…
Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a…
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…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator…
Chemical gradients can be used by a particle to determine its position. This \textit{positional information} is of crucial importance, for example in developmental biology in the formation of patterns in an embryo. The central goal of this…
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for it's manipulation in analogy with entanglement theory. In this…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
In stationary spacetimes global equilibrium states can be defined, applying the maximum entropy principle, by the introduction of local thermodynamic fields determined solely by geometry. As an example, we study a class of equilibrium…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…