Related papers: Question on Conditional Entropy
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…
A novel definition of the conditional smooth Renyi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Renyi entropy is appropriate to give lower and upper…
In this paper, we analyze the relationship between entropy and information in the context of the mixing process of two identical ideal gases. We will argue that entropy has a special information-based feature that is enfolded in the…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and…
We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be…
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
The standard conditional probability definition formula is derived as a consequence of the Insufficient Reason Principle expressed as the Maximum Relative Divergence Principle for grading (order-comonotonic) functions on a totally ordered…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
How to find unknown distributions is questioned in many pieces of research. There are several ways to figure them out, but the main question is which acts more reasonably than others. In this paper, we focus on the maximum entropy principle…
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…
Entropy serves as a central observable which indicates uncertainty in many chemical, thermodynamical, biological and ecological systems, and the principle of the maximum entropy (MaxEnt) is widely supported in natural science. Recently,…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore…
Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization,…
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by 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…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…