Uniform entropy vs topological entropy

Entropy operator for continuous dynamical systems of finite topological entropy

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.

Topological entropy

1. Definitions and general properties. Let X be a compact topological space. Definition 1. For any open cover 31 of X let N(ñ) denote the number of sets in a subco ver of minimal cardinality. A subco ver of a cover is minimal if no other subcover contains fewer members. Since X is compact and 31 is an open cover, there always exists a finite subcover. To conform with prior work in ergodic theor...

entropy operator for continuous dynamical systems of finite topological entropy

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.

Topological entanglement entropy.

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal densit...

Topological Entropy – A Survey