# Category: Entropy and information

Landauer's principle
Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such
Variation of information
In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely r
Joint entropy
In information theory, joint entropy is a measure of the uncertainty associated with a set of variables.
Rényi entropy
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
Mutual information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the
Entropy of network ensembles
A set of networks that satisfies given structural characteristics can be treated as a network ensemble. Brought up by Ginestra Bianconi in 2007, the entropy of a network ensemble measures the level of
Tsallis entropy
In physics, the Tsallis entropy is a generalization of the standard Boltzmann–Gibbs entropy.
Mean dimension
In mathematics, the mean (topological) dimension of a topological dynamical system is a non-negative extended real number that is a measure of the complexity of the system. Mean dimension was first in
Exformation
Exformation (originally spelled eksformation in Danish) is a term coined by Danish science writer Tor Nørretranders in his book The User Illusion published in English 1998. It is meant to mean explici
Binary entropy function
In information theory, the binary entropy function, denoted or , is defined as the entropy of a Bernoulli process with probability of one of two values. It is a special case of , the entropy function.
Topological entropy
In mathematics, the topological entropy of a topological dynamical system is a nonnegative extended real number that is a measure of the complexity of the system. Topological entropy was first introdu
Differential entropy
Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy, a measure of averag
Conditional mutual information
In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the va
Information fluctuation complexity
Information fluctuation complexity is an information-theoretic quantity defined as the fluctuation of information about entropy. It is derivable from fluctuations in the predominance of order and chao
Information content
In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random varia
Perplexity
In information theory, perplexity is a measurement of how well a probability distribution or probability model predicts a sample. It may be used to compare probability models. A low perplexity indicat
Nonextensive entropy
Entropy is considered to be an extensive property, i.e., that its value depends on the amount of material present. Constantino Tsallis has proposed a nonextensive entropy (Tsallis entropy), which is a
Principle of maximum caliber
The principle of maximum caliber (MaxCal) or maximum path entropy principle, suggested by E. T. Jaynes, can be considered as a generalization of the principle of maximum entropy. It postulates that th
Akaike information criterion
The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC es
Ascendency
Ascendency or ascendancy is a quantitative attribute of an ecosystem, defined as a function of the ecosystem's trophic network. Ascendency is derived using mathematical tools from information theory.
Negentropy
In information theory and statistics, negentropy is used as a measure of distance to normality. The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-scienc
Gibbs algorithm
In statistical mechanics, the Gibbs algorithm, introduced by J. Willard Gibbs in 1902, is a criterion for choosing a probability distribution for the statistical ensemble of microstates of a thermodyn
Measure-preserving dynamical system
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poin
Pointwise mutual information
In statistics, probability theory and information theory, pointwise mutual information (PMI), or point mutual information, is a measure of association. It compares the probability of two events occurr
Approximate entropy
In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data. For example, consider two series o
Kullback–Leibler divergence
In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution
Inequalities in information theory
Inequalities are very important in the study of information theory. There are a number of different contexts in which these inequalities appear.
Information gain ratio
In decision tree learning, Information gain ratio is a ratio of information gain to the intrinsic information. It was proposed by Ross Quinlan, to reduce a bias towards multi-valued attributes by taki
Minimum Discrimination Information
No description available.
Principle of maximum entropy
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precise
Maximum entropy probability distribution
In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. A
Entropy in thermodynamics and information theory
The mathematical expressions for thermodynamic entropy in the statistical thermodynamics formulation established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s are similar to the information en
Entropy estimation
In various science/engineering applications, such as independent component analysis, image analysis, genetic analysis, speech recognition, manifold learning, and time delay estimation it is useful to
Transfer entropy
Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. Transfer entropy from a process X to another pro
Cross entropy
In information theory, the cross-entropy between two probability distributions and over the same underlying set of events measures the average number of bits needed to identify an event drawn from the
Conditional entropy
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,
Entropy coding
In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which stat
Molecular demon
A Molecular demon or biological molecular machine is a biological macromolecule that resembles and seems to have the same properties as Maxwell's demon. These macromolecules gather information in orde
Partition function (mathematics)
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical
Entropy (information theory)
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variab