Related papers: A new definition of t-entropy for transfer operato…
Transfer entropy (TE) is an information theoretic measure that reveals the directional flow of information between processes, providing valuable insights for a wide range of real-world applications. This work proposes Transfer Entropy…
The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function.…
In the article, on a new definition of quantum entropy, Campisi has explained an operator for entropy based on quantum number operator. It has been claimed that the expectation values for this operator increases for every non-quasi-static…
We provide explicit bounds on the eigenvalues of transfer operators defined in terms of holomorphic data.
Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in transformations that are not isochoric (i.e.…
In this article we present a methodology to estimate the Transfer Entropy Rate between two systems through the Lempel-Ziv complexity. This methodology carries a set of practical advantages: it can be estimated from two single discrete…
Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
This article addresses the generation of the ETL operators(Extract-Transform-Load) for supplying a Data Warehouse from a relational data source. As a first step, we add new rules to those proposed by the authors of [1], these rules deal…
Transfer entropy is a widely used measure for quantifying directed information flows in complex systems. While the challenges of estimating transfer entropy for continuous data are well known, it has two major shortcomings for data of…
The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations…
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 consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods…
We give a definition of topological entropy for tree shifts, prove that the limit in the definition exists, and show that it dominates the topological entropy of the associated one-dimensional shift of finite type when the labeling of the…
We give a tentative definition of the recently introduced Root-$T\bar{T}$ operator in a generic, two dimensional quantum conformal field theory with continuous spectrum of scaling weights. The definition assumes certain factorization…
The purpose of this paper is to present a new class of operators known as polynomially hypo-EP operators, extending the notation of hypo-EP, $n$-hypo-EP, and polynomially EP. The paper explores numerous properties and characterizations of…
A recently proposed history formalism is used to define temporal entanglement in quantum systems, and compute its entropy. The procedure is based on the time-reduction of the history density operator, and allows a symmetrical treatment of…
Transfer entropy provides a general tool for analyzing the magnitudes and directions---but not the \emph{kinds}---of information transfer in a system. We extend transfer entropy in two complementary ways. First, we distinguish…
In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the…
We share a small connection between information theory, algebra, and topology - namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their…