相关论文: Introduction to Logical Entropy and its Relationsh…

This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a…

Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…

Entropy or information is a fundamental quantity contained in a system in statistical mechanics and information theory. In this paper, a definition of classical information entropy of parton distribution functions is suggested. The…

There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules…

Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…

In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a…

Shannon information theory provides various measures of so-called "syntactic information", which reflect the amount of statistical correlation between systems. In contrast, the concept of "semantic information" refers to those correlations…

Researchers have proposed formal definitions of quantitative information flow based on information theoretic notions such as the Shannon entropy, the min entropy, the guessing entropy, and channel capacity. This paper investigates the…

In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…

In this paper we formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we identify a comprehensive parallelism between information lattices and subgroup lattices.…

While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the…

In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…

The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of…

The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…

In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…

Currently, 'time' does not play any essential role in quantum information theory. In this sense, quantum information theory is underdeveloped similarly to how quantum physics was underdeveloped before Erwin Schrodinger introduced his famous…

According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and…

Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…