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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. The "fundamental problem ...
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 information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy. Named after Claude Shannon, the source coding theorem shows that ...
This equation gives the entropy in the units of "bits" (per symbol) because it uses a logarithm of base 2, and this base-2 measure of entropy has sometimes been called the shannon in his honor. Entropy is also commonly computed using the natural logarithm (base e, where e is Euler's number), which produces a measurement of entropy in nats per ...
The physical entropy may be on a "per quantity" basis (h) which is called "intensive" entropy instead of the usual total entropy which is called "extensive" entropy. The "shannons" of a message ( Η ) are its total "extensive" information entropy and is h times the number of bits in the message.
A misleading [1] information diagram showing additive and subtractive relationships among Shannon's basic quantities of information for correlated variables and . The area contained by both circles is the joint entropy H ( X , Y ) {\displaystyle \mathrm {H} (X,Y)} .
Entropy of a Bernoulli trial (in shannons) as a function of binary outcome probability, called the binary entropy function.. In information theory, the binary entropy function, denoted or (), is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability of one of two values, and is given by the formula:
The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by the Boltzmann constant).