相关论文: Anqie entropy and arithmetic compactification of n…
The paper introduces a (universal) C*-algebra of continuous functions vanishing at infinity on the n-dimensional quantum complex space. To this end, the well-behaved Hilbert space representations of the defining relations are classified.…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
We show that, if a simple $C^{*}$-algebra $A$ is topologically finite-dimensional in a suitable sense, then not only $K_{0}(A)$ has certain good properties, but $A$ is even accessible to Elliott's classification program. More precisely, we…
For certain groups, parabolic subgroups appear as stabilizers of flags of sets or vector spaces. Quotients by these parabolic subgroups represent orbits of flags, and their cardinalities asymptotically reveal entropies (as rates of…
The R\'enyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field $\lambda$ that controls the partition…
We introduce two notions of algebraic entropy for actions of cancellative right amenable semigroups $S$ on discrete abelian groups $A$ by endomorphisms; these extend the classical algebraic entropy for endomorphisms of abelian groups,…
It is known that the involution corresponding to the compact form is incompatible with comultiplication for quantum groups at $|q|=1$. In this paper we consider the quantum algebra of functions on the deformed space $T^{*}G_{q}$ which…
The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…
In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on…
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
In our previous paper [9], we have introduced topological nearly entropy, Ent_N (f) by restricting X into a class of nearly compact spaces. In the present paper, some additional properties of this notion are studied. Furthermore, we…
Extending our results in "Entropy conjecture for continuous maps of nilmanifolds", to appear in Israel Jour. of Math., we confirm that Entropy Conjecture holds for every continuous self-map of a compact $K(\pi,1)$ manifold with the…
We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well as various examples. The main result of…
We introduce a type of zero-dimensional dynamical system (a pair consisting of a totally disconnected compact metrizable space along with a homeomorphism of that space), which we call "fiberwise essentially minimal", and we prove that the…
Nuclear $C^*$-algebras having a system of completely positive approximations formed with convex combinations of a uniformly bounded number of order zero summands are shown to be approximately finite dimensional.
Let $E = (E^0, E^1, r, s)$ be a topological graph with no sinks such that $E^0$ and $E^1$ are compact. We show that when $C^*(E)$ is finite, there is a natural isomorphism $C^*(E) \cong C(E^\infty) \rtimes \mathbb{Z}$, where $E^\infty$ is…
We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where…