Related papers: A Coherent View on Entropy
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
This work is a discussion on the concept of information. We define here information as an abstraction that is able to be copied. We consider the connection between the process of copying information in quantum systems and the emergence of…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
In our previous articles ("The Information and the Matter", v1, v5; more systematically the informational conception is presented in arXiv paper "The Information as Absolute", 2010) it was rigorously shown that the Matter is some…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…
Projective measurement can increase the entropy of a state $\rho$, the increased entropy is not only up to the basis of projective measurement, but also has something to do with the properties of the state itself. In this paper we define…
The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to exploit this resource efficiently. We learn how to exploit entanglement efficiently by applying…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
I propose here a new concept of information based on two relevant aspects of its expression. The first related to the undeniable fact that the expression of information modifies the physical state of its receiver. The second to the…
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…
Shannon's metric of "Entropy" of information is a foundational concept of information theory. This article is a primer for novices that presents an intuitive way of understanding, remembering, and/or reconstructing Shannon's Entropy metric…