The method of types is a combinatorial method to evaluate probabilities via counting, that admits to derive asymptotically tight error bounds (primarily) for discrete memoryless models. The Budapest school of Information Theory, and specifically János Körner, had a decisive role in developing the underlying simple idea to a powerful general method. Its application has enabled us to solve (or ac...

This paper is motivated by an old and central problem in measurable dynamics: given two dynamical systems, determine whether or not they are measurably conjugate, i.e., isomorphic. Let us set some notation. A dynamical system (or system for short) is a triple (G,X, μ), where (X,μ) is a probability space and G is a group acting by measure-preserving transformations on (X,μ). We will also call th...

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

In this paper an example is given of a C2 map g from the circle onto itself, which permits an ß-explosion. It is shown that topological entropy (considered as a map from C2(Sl, S1) to the nonnegative real numbers) is continuous at g.

We derive a universal upper bound to the entropy of a charged system. The entropy bound follows from application of the generalized second law of thermodynamics to a gedanken experiment in which an entropy-bearing charged system falls into a charged black hole. This bound is stronger than the Bekenstein entropy bound for neutral systems. Black-hole physics mirrors thermodynamics in many respect...

We consider positive entropy G-systems for certain countable, discrete, infinite left-orderable amenable groups G. By undertaking local analysis, the existence of asymptotic pairs and chaotic sets will be studied in connecting with the stable sets. Examples are given for the case of integer lattice groups, the Heizenberg group, and the groups of integral unipotent upper triangular matrices.

It is known that for n ≥ 3 centres and positive energies the ncentre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy. Here we consider the energies above some threshold and show: Whereas for arbitrary g > 1 independent integrals of Gevrey class g exist, no real-analytic (that is, Gevrey class 1) independent integral exists.

The entropy conjecture for tori has been settled a long time ago by Misiurewicz and Przytycki. We show that their result extends from tori to compact and connected abelian groups. We give stronger results for hyperbolic automorphisms. Throughout this paper G denotes a compact and connected metric abelian group. The group operation on G is written additively.

It is widely argued that the spectacular local decreases in entropy that occurred on Earth as a result of the origin and evolution of life and the development of human intelligence are not inconsistent with the second law of thermodynamics, because the Earth is an open system and entropy can decrease in an open system, provided the decrease is compensated by entropy increases outside the system...