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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. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel , and a receiver.
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
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
Many of the concepts in information theory have separate definitions and formulas for continuous and discrete cases. For example, entropy is usually defined for discrete random variables, whereas for continuous random variables the related concept of differential entropy, written (), is used (see Cover and Thomas, 2006, chapter 8).
This quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. [9] In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory.
The mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information. The choice of logarithmic base in the following formulae determines the unit of information entropy that is used.
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 .
In this context, either an information-theoretical measure, such as functional clusters (Gerald Edelman and Giulio Tononi's functional clustering model and dynamic core hypothesis (DCH) [47]) or effective information (Tononi's integrated information theory (IIT) of consciousness [48] [49] [50]), is defined (on the basis of a reentrant process ...