Related papers: Dynamical systems and computable information
Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we provide a…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
In this paper, I propose a theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, I present an information-geometric…
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…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy…
We consider Hamiltonian quantum systems with energy bandwidth \Delta E and show that each measurement that determines the time up to an error \Delta t generates at least the entropy (\hbar/(\Delta t \Delta E))^2/2. Our result describes…
Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and…
We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a…
Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Commonly, the notion of "quantum chaos'' refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
The statistical properties of physical systems in thermal equilibrium are blatantly different from their far-from-equilibrium counterparts. In the latter, fluctuations often dominate the dynamics and might cluster in ordered patterns in the…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Bohr chaoticity is a topological notion of dynamical complexity defined through non-orthogonality to all non-trivial weights. It is strictly stronger than positivity of topological entropy and also has strong consequences for the…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…