Related papers: A new definition of t-entropy for transfer operato…
It is supposed that the exponential multiplier in the method of the non-equilibrium statistical operator (Zubarev`s approach) can be considered as a distribution density of the past lifetime of the system, and can be replaced by an…
By generalizing the density matrix to a transition matrix between two states, represented as $|\phi\rangle$ and $|\psi\rangle$, one can define the pseudoentropy analogous to the entanglement entropy. In this paper, we establish an operator…
The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…
This paper is the second part of a previous paper (Marquet, 2019) dealing with the need to define the entropy with an absolute way, by using the third law of thermodynamics. In this second part it is shown that there is a need and interest…
This manuscript introduces a computationally efficient method to calculate the nonlinearity of a quantum feature map, as well as a method for determining whether a quantum feature map will have a high concentration of quantum states. The…
We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
We provide upper bounds for entropy numbers for two types of operators: summation operators on binary trees and integral operators of Volterra type. Our efforts are concentrated on the critical cases where none of known methods works.…
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…
This short note contains a list of new results concerning the R\'{e}nyi entropy, the Tsallis entropy, and the Heun functions associated with positive linear operators.
The celebrated Trotter approximation theorem provides a sufficient condition for the convergence of a sequence of operator semigroups in terms of the corresponding sequence of infinitesimal generators. There exist a few results on the rate…
Astrophysical transient phenomena are traditionally classified spectroscopically in a hierarchical taxonomy; however, this graph structure is currently not utilized in neural net-based photometric classifiers for time-domain astrophysics.…
Using follower/predecessor/extender set sequences, we define quantities which we call the follower/predecessor/extender entropies, which can be associated to any shift space. We analyze the behavior of these quantities under conjugacies and…
We present an operational semantics for the language MeTTa.
We give a necessary and sufficient condition for transport-entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verifying Talagrand's T2 inequality and not the logarithmic…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…
This paper is an introduction to the von Neumann entropy in a historic approach. Von Neumann's gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. In the analysis of his ideas we…
The ability to quantify the directional flow of information is vital to understanding natural systems and designing engineered information-processing systems. A widely used measure to quantify this information flow is the transfer entropy.…
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…