We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.

We show that a class of robustly transitive diffeomorphisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have constant entropy and isomorphic unique measures of maximal entropy.

Abstract We give a finitary criterion for the convergence of measures on non-elementary geometrically finite hyperbolic orbifolds to unique measure maximal entropy. an entropy controlling escape mass cusps orbifold. Using this criterion, we prove new results distribution collections closed geodesics such orbifold, and as corollary, equidistribution up certain length in amenable regular covers o...

Let {T t} be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let μ be an ergodic measure of maximal entropy. We show that either {T t} is Bernoulli, or {T t} is isomorphic to the product of a Bernoulli flow and a rotational flow. Applications are given to Reeb flows.

We study L-systems whose main operators are extensions of one-dimensional half-line Schr\"odinger with deficiency indices $(1, 1)$, the L-systems. Introducing new concepts an c-entropy and dissipation coefficient for L-system we discuss following dual problems: describe (1) a given minimal coefficient, (2) maximal c-entropy. Also, analyze in detail problems sectorial extremal operators.

Using donor-controlled, bottom-up equations to describe network collapse we systematically investigate the impact each species has on the survival or extinction of other species. Short of extinction, one can determine the integrated losses experienced by the ecosystem. These losses are aggregated into system level indicators, such as entropy, average gain/loss, average time to extinction, etc. ...

In this article we discuss relations between algebraic and dynamical properties of non-cyclic semigroups rational maps.

We introduce the maximal correlation coefficient R(M1,M2) between two noncommutative probability subspaces M1and M2 and show that sub-algebras generated by sn:=x1+…+xnand sm:=x1+…+xm equals m∕n for m≤n, where (xi)i∈N is a sequence of free identically distributed random variables. This free-probability analogue result Dembo–Kagan–Shepp in classical probability. As an application, we use this est...