Related papers: Generalized Derangetropy Functionals for Modeling …
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be…
We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
We develop a structural theory of information backflow in minimal non-Markovian relaxation processes within the framework of nonequilibrium statistical mechanics. The approach is based on the time-convolution (TC) and time-convolutionless…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
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…
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a…
We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These…
An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…
We present a possible approach to the study of the renormalization group (RG) flow based entirely on the information theory. The average information loss under a single step of Wilsonian RG transformation is evaluated as a conditional…
We propose R\'enyi information generating function and discuss its properties. A connection between the R\'enyi information generating function and the diversity index is proposed for discrete type random variables. The relation between the…
In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…
We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is continuously generated in an auxiliary…
The $n$-index R\'enyi mutual information and transfer entropy for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of thermodynamic quantities. By means of Monte…
Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
We derive three fundamental decompositions on relevant information quantities in feedback systems. The feedback systems considered in this paper are only restricted to be causal in time domain and the channels are allowed to be subject to…