We show that a certain type of conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also consider distribution asymptotics of information; e.g. for Boole’s transformation, information is asymptotically mod-normal, a property shared by certain ergodic, probability preserving transformations with zero entropy. §0 Intr...

Zurek, Habib, and Paz @Phys. Rev. Lett. 70, 1187 ~1993!# have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment and shown that coherent states are maximal for the particular environment model examined. To generalize these results, I consider entropy production within the Lindblad theory of ope...

Based on an intuitionistic knowledge content nature of information gain, the concept of combination entropy CE(A) in incomplete information systems is first introduced, and some of its important properties are given. Then, the conditional combination entropy CE(Q | P ) and the mutual information CE(P ;Q) are defined. Unlike all existing measures for the uncertainty in incomplete information sys...

We prove that for a class of Zd shifts of finite type, d > 1, any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.

The information entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objects and the analysis of information systems. The information entropy of a partition is non-increasing when the partition is refined, and is related to rough sets by Wong and Ziarko. The partitions and information entropy have some graph-theoreti...

We study various mixing properties for subshifts, which allow words in the language to be concatenated into a new word in the language given certain gaps between them. All are defined in terms of an auxiliary gap function f : N → N, which gives the minimum required gap length as a function of the lengths of the words on either side. In this work we focus mostly on topological transitivity, topo...

We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy configurations unlike Shannon entropy. We discuss how, beginning with quantum entanglement of microsystems with one another and with the environment, one can obtain...

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p > 1, the minimum output Rényi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Rényi entropy of order p for a product channel need not be significantly greater than the minimum output entr...