Related papers: Entropy in a category

To an exact endofunctor of a triangulated category with a split-generator, the notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which is a (possibly negative infinite) real-valued function of a real variable. In this…

In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…

We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we…

The main purpose of this article is to provide a common generalization of the notions of a topological and Kolmogorov-Sinai entropy for arbitrary representations of discrete amenable groups on objects of (abstract) categories. This is…

Let A be a finitely presented associative monomial algebra. We study the category qgr(A) which is a quotient of the category of graded finitely presented A-modules by the finite-dimensional ones. As this category plays a role of the…

Building on the author's earlier work on topological and abstract expansivity, this paper introduces and explores the notion of algebraic expansivity for endomorphisms of abelian groups. We analyze the fundamental properties of this…

A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of…

Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of the endofunctor. Computing the entropy of the composition of…

Over the past few years the understanding of the microscopic theory of black hole entropy has made important conceptual progress by recognizing that the degeneracies are encoded in partition functions which are determined by higher rank…

This article contains a review of categorifications of semisimple representations of various rings via abelian categories and exact endofunctors on them. A simple definition of an abelian categorification is presented and illustrated with…

We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…

We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented…

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…

L\'{a}szl\'{o} Fuchs posed the following question: which abelian groups arise as the group of units in a ring? In this paper, we investigate a related question: for such realizable groups $G$, when is there a ring $R$ with unit group $G$…

We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories,…

It is shown that if (M,phi,alpha) is a W*-dynamical system with M a type I von Neumann algebra then the entropy of alpha w.r.t. phi equals the entropy of the restriction of alpha to the center of M. If furthermore (N,psi,beta) is a…

This short book is an elementary course on entropy, leading up to a calculation of the entropy of hydrogen gas at standard temperature and pressure. Topics covered include information, Shannon entropy and Gibbs entropy, the principle of…

In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…