Related papers: Isomorphism between Maximum Lyapunov Exponent and …
One of the key aspects of Shannon's theory is that it provides guidance for designing the most efficient systems, such as minimizing errors and clarifying the limits of coding. Such theories have made great developments in the 50 years…
Shannon's theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly, and in the presence of various resources that are all classes of non-signalling correlations:…
The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed…
The interactive capacity of a noisy channel is the highest possible rate at which arbitrary interactive protocols can be simulated reliably over the channel. Determining the interactive capacity is notoriously difficult, and the best known…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
We investigate the dependence of the largest Lyapunov exponent of a $N$-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition…
Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication…
We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its…
We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows…
Isomorph theory is one of the promising theories to understand the quasi-universal relationship between thermodynamic, dynamic and structural characteristics. Based on the hidden scale invariance of the inverse power law potentials, it…
For a fast particle moving within a two-dimensional array of soft scatterers - centers of weak and short-range potential - the dependence of the Lyapunov exponent on the system parameters is studied. The use of the linearized equations for…
Similar to the energy flowing process in traditional heat engines, information could be considered to flow in the communication systems with the form of energy and entropy. Combining the thermodynamic Carnot machine and the classical…
We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho(p,q)$. Of particular interest is $\lambda_2$, an exponent which quantifies the rate at which chaotically evolving…
A framework is presented for unsupervised learning of representations based on infomax principle for large-scale neural populations. We use an asymptotic approximation to the Shannon's mutual information for a large neural population to…
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two…
Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest exponent is a measure of the time horizon over which the evolution of the system can be…
As conventional communication systems based on classic information theory have closely approached the limits of Shannon channel capacity, semantic communication has been recognized as a key enabling technology for the further improvement of…
The asymptotic rates of information-theoretic protocols - including error exponents, compression rates, and channel capacities - are traditionally defined under the idealised assumption that the underlying resource (state or channel) is…
We calculate the maximal Lyapunov exponent, the generalized entropies, the asymptotic distance between nearby trajectories and the fractal dimensions for a finite two dimensional system at different initial excitation energies. We show that…
Classically, no information can be transmitted through a depolarising, that is a completely noisy, channel. We show that by combining a depolarising channel with another channel in an indefinite causal order---that is, when there is…