Related papers: Exponential state estimation, entropy and Lyapunov…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Shannon entropy is often a quantity of interest to linguists studying the communicative capacity of human language. However, entropy must typically be estimated from observed data because researchers do not have access to the underlying…
This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…
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…
It is supposed that the exponential multiplier in the method of the non-equilibrium statistical operator (Zubarev`s approach) can be considered as a distribution density of the past lifetime of the system, and can be replaced by an…
We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…
The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
In this paper we study ergodic optimization problems for subadditive sequences of functions on a topological dynamical system. We prove that for $t\rightarrow \infty$ any accumulation point of a family of equilibrium states is a maximizing…
We study the problem of remote state estimation, in the presence of an eavesdropper. An authorized user estimates the state of a linear plant, based on the data received from a sensor, while the data may also be intercepted by the…
Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…
The rate of change of entropy $\dot S$ is measured for a system of particles floating on the surface of a fluid maintained in a turbulent steady state. The resulting coagulation of the floaters allows one to relate $\dot S$ to the velocity…
We compare an entropy estimator $H_z$ recently discussed in [10] with two estimators $H_1$ and $H_2$ introduced in [6][7]. We prove the identity $H_z \equiv H_1$, which has not been taken into account in [10]. Then, we prove that the…
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment…