Related papers: Algebraic entropy for algebraic maps
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
We define entropy invariants for abstract algebraic structures using an asymptotic Boltzmann formula.
The notion of intrinsic algebraic entropy of an endomorphism of a given Abelian group has been recently introduced in [D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (2015)…
In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a…
In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are reproved using elementary…
In this paper, the concept of L-algebra is revisited and after that, the article is prepared to deal with the notion of the entropy of an L-algebra. If a set has an L-algebraic structure, it is possible to calculate the degree of…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra…
The common in ring, module and algebra is that they are Abelian group with respect to addition. This property is enough to study integration. I treat integral of measurable map into normed Abelian $\Omega$-group. Theory of integration of…
We give a numerical characterization of mutual orthogonality (that is, complementarity) for subalgebras. In order to give such a characterization for mutually orthogonal subalgebras $A$ and $B$ of the $k \times k$ matrix algebra…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic…
In this paper, we mainly consider on the entropy of the extended map conditional to the natural extension of a dynamical system for an Abelian group action and we calculate the entropy is zero.
In this paper, we introduce the notion of relative ultragraph algebras and extend classical injectivity criteria for representations, particularly those arising from branching systems,to this relative setting. This new concept is closely…
The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…