In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

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, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

introduction the chemical characteristic of groundwater as a major source of water supply for human life is an important factor in determining the usage of it for agriculture, industry and drinking. useful techniques and different methods of studying the chemical composition of groundwater such as correlation coefficient, descriptive statistics, factor analysis and cluster analysis provide an u...

The present study carefully examined entropy generation during wustite pellet reduction to sponge iron. The finite volume method was used to solve the governing equations. The grain model was used to simulate the reaction rate. The reactant gases including carbon monoxide and hydrogen were converted to water and carbon dioxide after wustite reduction. Entropy is generated by heat transfer, mass...

congestive heart failure (chf) remains to be one of the major cardiovascular disorders in the world. due to the prevalence of chf related issues, it is prudent to seek out new prognostic predictors that would facilitate the prevention, monitoring, and treatment of the disease on a daily basis. a detection approach using entropy measures extracted from surface electrocardiograms (ecgs) and class...

In this paper we study some monotone behavior of the residual (past) entropy of order . We prove that, under some relation between the hazard rates (reversed hazard rates) of two distributions functions F and G, when the residual (past) entropy of order of F is decreasing (increasing) then the residual (past) entropy of G is decreasing (increasing). Using this, several conclusions regarding mo...