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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 ...
The "shannons" of a message (Η) are its total "extensive" information entropy and is h times the number of bits in the message. A direct and physically real relationship between h and S can be found by assigning a symbol to each microstate that occurs per mole, kilogram, volume, or particle of a homogeneous substance, then calculating the 'h ...
The special case of information entropy for a random variable with two outcomes is the binary entropy function, usually taken to the logarithmic base 2, thus having the shannon (Sh) as unit: H b ( p ) = − p log 2 p − ( 1 − p ) log 2 ( 1 − p ) . {\displaystyle H_{\mathrm {b} }(p)=-p\log _{2}p-(1-p)\log _{2}(1-p).}
If the base of the logarithm is 2, then the unit of uncertainty is the shannon (more commonly known as bit). If it is the natural logarithm, then the unit is the nat. Hartley used a base-ten logarithm, and with this base, the unit of information is called the hartley (aka ban or dit) in his honor. It is also known as the Hartley entropy or max ...
[1] The shannon also serves as a unit of the information entropy of an event, which is defined as the expected value of the information content of the event (i.e., the probability-weighted average of the information content of all potential events). Given a number of possible outcomes, unlike information content, the entropy has an upper bound ...
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 and disorder also have associations with equilibrium. [8] Technically, entropy, from this perspective, is defined as a thermodynamic property which serves as a measure of how close a system is to equilibrium—that is, to perfect internal disorder. [9]
The Shannon entropy of the random variable above is defined as = = = [ ()], by definition equal to the expected information content of measurement of . [ 3 ] : 11 [ 4 ] : 19–20 The expectation is taken over the discrete values over its support .