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Generally, information entropy is the average amount of information conveyed by an event, when considering all possible outcomes. The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", [2] [3] and is also referred to as Shannon entropy.
The defining expression for entropy in the theory of information established by Claude E. Shannon in 1948 is of the form: = , where is the probability of the message taken from the message space M, and b is the base of the logarithm used.
Other important information theoretic quantities include the Rényi entropy and the Tsallis entropy (generalizations of the concept of entropy), differential entropy (a generalization of quantities of information to continuous distributions), and the conditional mutual information.
Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory.
According to the Big Bang theory, the Universe was initially very hot with energy distributed uniformly. For a system in which gravity is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into black holes, a state to which the system may eventually evolve). As the ...
Thermodynamic entropy is equal to the Boltzmann constant times the information entropy expressed in nats. The information entropy expressed with the unit shannon (Sh) is equal to the number of yes–no questions that need to be answered in order to determine the microstate from the macrostate. The concepts of "disorder" and "spreading" can be ...
To be distinguished from: Category:Thermodynamic entropy, for articles relating to entropy specifically in a thermodynamic context. Articles relating to entropy should generally be placed in one or the other of these categories, but not both (the main exception being Entropy in thermodynamics and information theory ).
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons , nats , or hartleys .