相关论文: Dynamical systems and computable information

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…

It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…

Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…

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…

The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…

It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…

Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of "phase" based on the standard concept of order…

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…

Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data…

Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a…

A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…

Coarse-grained measurements offer a scalable alternative to full state tomography for characterizing complex quantum dynamics. We show that observational entropy (OE), an information-theoretic entropy defined directly from finite-resolution…

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…

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

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…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…

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 propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that…