Related papers: Information-theoretic formulation of dynamical sys…
This paper introduces a framework for modeling cyclical and feedback-driven information flow through a generalized family of entropy-modulated transformations called derangetropy functionals. Unlike scalar and static entropy measures such…
Observing and controlling complex networks are of paramount interest for understanding complex physical, biological and technological systems. Recent studies have made important advances in identifying sensor or driver nodes, through which…
What is information, physically, and why does it so reliably emerge in living, cultural, and technological systems? Existing theories quantify uncertainty, cost, or compressibility, but do not identify which physical structures count as…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Life is fundamentally a scientific enigma. The interplay between chaos, entropy dynamics, and Prigogine's dissipative systems offers profound insights into the emergence, stabilization, and eventual collapse of far-from-equilibrium systems.…
Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a…
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…
During the last two decades, concentration of measure has been a subject of various exciting developments in convex geometry, functional analysis, statistical physics, high-dimensional statistics, probability theory, information theory,…
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…
A thermodynamic framework for asymptotic inference is developed in which sample size and parameter variance define a state space. Within this description, Shannon information plays the role of entropy, and an integrating factor organizes…
Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…
Recent developments enable the quantification of causal control given a structural causal model (SCM). This has been accomplished by introducing quantities which encode changes in the entropy of one variable when intervening on another.…
Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
The hallmark of deterministic chaos is that it creates information---the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a…