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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.
Common values of b are 2, Euler's number e, and 10, and the unit of entropy is shannon (or bit) for b = 2, nat for b = e, and hartley for b = 10. [ 1 ] Mathematically H may also be seen as an average information, taken over the message space, because when a certain message occurs with probability p i , the information quantity −log( p i ...
Shannon originally wrote down the following formula for the entropy of a continuous distribution, known as differential entropy: = ().Unlike Shannon's formula for the discrete entropy, however, this is not the result of any derivation (Shannon simply replaced the summation symbol in the discrete version with an integral), and it lacks many of the properties that make the discrete entropy a ...
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).
In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi , who looked for the most general way to quantify information while preserving additivity for independent events.
The Boltzmann constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J⋅K −1) in the International System of Units (or kg⋅m 2 ⋅s −2 ⋅K −1 in terms of base units). The entropy of a substance is usually given as an intensive property — either entropy per unit mass ...
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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 .