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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 .
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 ...
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.
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 ...
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).
The limitations of the random walker Shannon entropy can be overcome by adapting it to use a Kolmogorov–Sinai entropy. In this context, network entropy is the entropy of a stochastic matrix associated with the graph adjacency matrix ( A i j ) {\displaystyle (A_{ij})} and the random walker Shannon entropy is called the dynamic entropy of the ...
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 ...