Related papers: Which entropy for general physical theories?
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
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…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
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…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
The Shannon entropy of a collection of random variables is subject to a number of constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question to decide which of these "laws of information…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…
We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…
The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its…