Related papers: Information, complexity and entropy: a new approac…
The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to the Kolmogorov's entropy, complexity and…
It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable group actions. Namely, for an ergodic shift-action, the…
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are…
We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…
We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic…
Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…