相关论文: Isomorphism between Maximum Lyapunov Exponent and …

Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic…

Shannon's Capacity Theorem is the main concept behind the Theory of Communication. It says that if the amount of information contained in a signal is smaller than the channel capacity of a physical media of communication, it can be…

We present a general formalism for computing the largest Lyapunov exponent and its fluctuations in spatially extended systems described by diffusive fluctuating hydrodynamics, thus extending the concepts of dynamical system theory to a…

Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…

This paper focuses on a fundamental inquiry in a coupled oscillator model framework. It specifically addresses the direction of net information flow in mutually coupled non-identical chaotic oscillators. Adopting a specific form of…

Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical…

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment…

We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover,…

Information transfer through electromagnetic waves is an important problem that touches a variety of technologically relevant applications, including computing and telecommunications. Prior attempts to establish limits on optical…

Does semantic communication require a semantic information theory parallel to Shannon's information theory, or can Shannon's work be generalized for semantic communication? This paper advocates for the latter and introduces a semantic…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56},…

The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical…

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…

The Ising spin chain with longitudinal and transverse magnetic fields is often used in studies of quantum chaos, displaying both chaotic and integrable regions in its parameter space. However, even at a strongly chaotic point this model…

Using direct numerical simulation we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully…

In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory the no-cloning theorem means that noiseless copying and feedback of quantum…

We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode…

By performing a large number of fully resolved simulations of incompressible homogeneous and isotropic two dimensional turbulence, we study the scaling behavior of the maximal Lyapunov exponent, the Kolmogorov-Sinai entropy and attractor…

The maximum Lyapunov exponent (referred to the mean half-period of phase libration) of the motion in the chaotic layer of a nonlinear resonance subject to symmetric periodic perturbation, in the limit of infinitely high frequency of the…