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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…

Nuclear Theory · Physics 2008-11-26 F. Gulminelli , Ph. Chomaz , O. Juillet , M. J. Ison , C. O. Dorso

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum…

chao-dyn · Physics 2007-05-23 Hugo Touchette , Seth Lloyd

Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…

Information Theory · Computer Science 2025-04-23 Aaron J. Gutknecht , Fernando E. Rosas , David A. Ehrlich , Abdullah Makkeh , Pedro A. M. Mediano , Michael Wibral

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…

Statistical Mechanics · Physics 2009-11-13 Piotr Garbaczewski

Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called…

Robotics · Computer Science 2013-07-19 Georg Martius , Ralf Der , Nihat Ay

We extend present Shannon's static statistical information theory to dynamic processes and establish a dynamic statistical information theory. We derive the nonlinear evolution equations of dynamic information density and dynamic…

Statistical Mechanics · Physics 2007-05-23 Xing Xiu-San

Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…

Information Theory · Computer Science 2025-12-08 El Mahdi Mouloua , Essaid Mohamed

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…

Statistical Mechanics · Physics 2009-11-11 E. V. Vakarin , J. P. Badiali

This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…

Biomolecules · Quantitative Biology 2007-05-23 Christoph Adami

Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…

Information Theory · Computer Science 2020-01-17 Jed A. Duersch , Thomas A. Catanach

Although compartmental dynamical systems are used in many different areas of science, model selection based on the maximum entropy principle (MaxEnt) is challenging because of the lack of methods for quantifying the entropy for this type of…

Information Theory · Computer Science 2023-08-23 Holger Metzler , Carlos A. Sierra

We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal…

Statistical Mechanics · Physics 2015-05-19 James P. Crutchfield , Christopher J. Ellison , Ryan G. James , John R. Mahoney

We develop information theory for the temporal behavior of memoryful agents moving through complex -- structured, stochastic -- environments. We introduce and explore information processes -- stochastic processes produced by cognitive…

Statistical Mechanics · Physics 2025-08-04 James P. Crutchfield , Alexandra Jurgens

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

Fluid Dynamics · Physics 2018-02-23 Andrew J. Majda , Di Qi

We study analysis of complex systems using a Quantitative Theory of Meaning developed as an extention of Shannon's Communication Theory. The approach consideres complexity not in terms of the manifestation of its effects which are…

Computers and Society · Computer Science 2024-12-13 Inga Ivanova , John S. Torday

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…

Statistical Mechanics · Physics 2016-06-20 Ryan G. James , Nix Barnett , James P. Crutchfield

Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…

Fluid Dynamics · Physics 2019-04-23 T. -W. Lee

Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused on the source-channel-receiver problem and on the asymptotic limits of accuracy and…

Adaptation and Self-Organizing Systems · Physics 2017-05-16 Nicolás Rubido , Celso Grebogi , Murilo S. Baptista

Shannon's information entropy measures of the uncertainty of an event's outcome. If learning about a system reflects a decrease in uncertainty, then a plausible intuition is that learning should be accompanied by a decrease in the entropy…

Robotics · Computer Science 2015-02-20 Paul E. Smaldino

We consider a general N-degree-of-freedom nonlinear Hamiltonian system which is chaotic and dissipative and show that the origin of chaotic diffusion lies in the correlation of fluctuation of linear stability matrix for the equation of…

chao-dyn · Physics 2009-10-31 Bidhan Chandra Bag , Jyotipratim Ray Chaudhuri , Deb Shankar Ray