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Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally, information entropy is the average amount of information conveyed by an event, when considering all ...
Additionally, the relationship between energy and information formulated by Brillouin has been proposed as a connection between the amount of bits that the brain processes and the energy it consumes: Collell and Fauquet [12] argued that De Castro [13] analytically found the Landauer limit as the thermodynamic lower bound for brain computations ...
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include: In search engine technology, mutual information between phrases and contexts is used as a feature for k-means clustering to discover semantic clusters (concepts). [31]
To do this, one must acknowledge the difference between the measured entropy of a system—which depends only on its macrostate (its volume, temperature etc.)—and its information entropy, [6] which is the amount of information (number of computer bits) needed to describe the exact microstate of the system.
The Kullback–Leibler divergence (or information divergence, information gain, or relative entropy) is a way of comparing two distributions: a "true" probability distribution , and an arbitrary probability distribution .
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 statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microscopic states that constitute ...
For example, if there is a one-in-a-million chance of Alice winning the lottery, her friend Bob will gain significantly more information from learning that she won than that she lost on a given day. (See also Lottery mathematics.) This establishes an implicit relationship between the self-information of a random variable and its variance.