Abstmct-In his original paper on the subject, Shannon found upper and lower bounds for the entropy of printed English based on the number of trials required for a subject to guess subsequent symbols in a given text. The guessing approach precludes asymptotic consistency of either the upper or lower bounds except for degenerate ergodic processes. Shannon’s technique of guessing the next symbol i...

We test perturbatively a recent scheme for implementing chiral fermions on the lattice, proposed by Kaplan and modified by Narayanan and Neuberger, using as our testing ground the chiral Schwinger model. The scheme is found to reproduce the desired form of the effective action, whose real part is gauge invariant and whose imaginary part gives the correct anomaly in the continuum limit, once tec...

Estimating the entropy of finite strings has applications in areas such as event detection, similarity measurement or in the performance assessment of compression algorithms. This report compares a variety of computable information measures for finite strings that may be used in entropy estimation. These include Shannon’s n-block entropy, the three variants of the Lempel-Ziv production complexi...

The goal of this paper is to show the dependency of measured entropy of English text on subject of the experiment, the type of English text, and the methodology used to estimate the entropy.

We provide a new inequality that links two important entropy notions: Shannon Entropy H1 and collision entropy H2. Our formula gives the worst possible amount of collision entropy in a probability distribution, when its Shannon Entropy is fixed. While in practice it is easier to evaluate Shannon entropy than other entropy notions, it is well known in folklore that it does not provide a good est...

We consider a prototypical nonlinear reaction-diffusion system arising in reversible chemistry. Based on recent existence results of global weak and classical solutions derived from entropy-decay related apriori estimates and duality methods, we prove exponential convergence of these solutions towards equilibrium with explicit rates in all space dimensions. The key step of the proof establishes...

We estimate the dynamical entropy for the quantized CAT map. It turns out that the result depends on the rotation parameter and positivity of the dynamical entropy demands asymptotic abelianness. Further the estimates ooer a counterexample to the additivity of the dynamical entropy for tensor products.

In this project, bridging entropy econometrics, game theory and information theory, a game theoretic approach will be investigated to quantum information, during which new mathematical definitions for quantum relative entropy, quantummutual information, and quantum channel capacity will be given and monotonicity of entangled quantum relative entropy and additivity of quantum channel capacity wi...

We estimate the entropy associated to a background of squeezed cosmic gravitons, and we argue that the process of cosmological pair production from the vacuum may explain the large amount of entropy of our present universe.