Related papers: The topological version of free entropy
We discuss free probability theory and free harmonic analysis from a categorical perspective. In order to do so, we extend first the set of analytic convolutions and operations and then show that the comonadic structure governing free…
The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…
We present a brief introduction to analytic capacity, with an emphasis on its numerical computation. We also discuss several related open problems.
This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical as well as some newer entropy notions to a broad audience with an intermediate background in dynamical…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
Let {\phi} be an automorphism on a connected Lie group G. Through several G-subgroups associated to the dynamics of {\phi} we analyze their topological entropy. Assume that G belongs to the class of finite semisimple center Lie groups which…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
Aided by the tools and outlook provided by modern classification theory, we take a new look at the Brown-Voiculescu entropy of endomorphisms of nuclear C*-algebras. In particular, we introduce `coloured' versions of noncommutative…
This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational…
The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free…
In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find…
In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.
We compute free energies as well as conformal anomalies associated with boundaries for a conformal free scalar field. To that matter, we introduce the family of spaces of the form $\mathbb{S}^a\times \mathbb{H}^b$, which are conformally…
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…
In this paper, entropies, including measure-theoretic entropy and topological entropy, are considered for random $\mathbb{Z}^k$-actions which are generated by random compositions of the generators of $\mathbb{Z}^k$-actions. Applying Pesin's…
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…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
In this work we construct from ground up a homotopy theory of C*-algebras. This is achieved in parallel with the development of classical homotopy theory by first introducing an unstable model structure and second a stable model structure.…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…