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Average uncertainty in variable's states
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential
Entropy_(information_theory)
Relationship between the concepts of thermodynamic entropy and information entropy
k_{B}} is the Boltzmann constant. The defining expression for entropy in the theory of information established by Claude E. Shannon in 1948 is of the form:
Entropy in thermodynamics and information theory
Entropy_in_thermodynamics_and_information_theory
Measure of distance to normality
In information theory and statistics, negative entropy is used as a measure of distance to normality. It is also known as negentropy or syntropy. It is
Negentropy
Measure of relative information in probability theory
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y {\displaystyle
Conditional_entropy
Concept in information theory
In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision
Rényi_entropy
Topics referred to by the same term
the adiabatic constant Entropy (information theory), also called Shannon entropy, a measure of the unpredictability or information content of a message
Entropy_(disambiguation)
Time density of the average information in a stochastic process
In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the
Entropy_rate
Scientific study of digital information
the outcome after the coin has landed, the entropy is zero because you have gained one bit. Information theory has been used in a wide range of applications
Information_theory
Part of the history of physics
coined the term entropy. Since the mid-20th century, the concept of entropy has found application in the field of information theory, describing an analogous
History_of_entropy
Concept in information theory
Differential entropy (also referred to as continuous entropy) in information theory is a property of absolutely continuous probability distributions which
Differential_entropy
Mathematical statistics distance measure
distance Information gain in decision trees Information gain ratio Information theory and measure theory Jensen–Shannon divergence Quantum relative entropy Solomon
Kullback–Leibler_divergence
Lossless data compression scheme
In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared
Entropy_coding
Measure of dependence between two variables
concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the
Mutual_information
Measure of information in probability and information theory
In information theory, joint entropy is a measure of the uncertainty associated with a set of variables. The joint Shannon entropy (in bits) of two discrete
Joint_entropy
Concept
In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced
Entropy (statistical thermodynamics)
Entropy_(statistical_thermodynamics)
Theory in modern physics that describes gravity as an entropic force
Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an entropic force—a force with macro-scale homogeneity
Entropic_gravity
In information theory, the entropy power inequality (EPI) is a result that relates to so-called "entropy power" of random variables. It shows that the
Entropy_power_inequality
Principle in Bayesian statistics
arguing that the entropy of statistical mechanics and the information entropy of information theory are the same concept. Consequently, statistical mechanics
Principle_of_maximum_entropy
Entropy of a process with only two probable values
In information theory, the binary entropy function, denoted H ( p ) {\displaystyle \operatorname {H} (p)} or H b ( p ) {\displaystyle \operatorname
Binary_entropy_function
Property of a thermodynamic system
in cosmology, economics, and information systems including the transmission of information in telecommunication. Entropy is central to the second law
Entropy
Application of information theory to thermodynamics and statistical mechanics
inference techniques rooted in Shannon information theory, Bayesian probability, and the principle of maximum entropy. These techniques are relevant to any
Maximum entropy thermodynamics
Maximum_entropy_thermodynamics
Principle in theoretical physics
used measure of information content, now known as Shannon entropy. As an objective measure of the quantity of information, Shannon entropy has been enormously
Holographic_principle
Probability distribution that has the most entropy of a class
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
Maximum entropy probability distribution
Maximum_entropy_probability_distribution
Information held in the state of a quantum system
using quantum information processing techniques. Quantum information refers to both the technical definition in terms of von Neumann entropy and the general
Quantum_information
Computer data measurements and scales
Entropy in thermodynamics and information theory. Entropy (information theory), such as the amount of information that can be stored in DNA Entropy (thermodynamics)
Orders_of_magnitude_(data)
Notion in statistics
information Quantum Fisher information White information matrix test Other measures employed in information theory: Entropy (information theory) Kullback–Leibler
Fisher_information
Dudley's entropy integral is a mathematical concept in the field of probability theory that describes a relationship involving the entropy of certain
Dudley's_entropy_integral
uncertainty) entropy encoding entropy (information theory) Fisher information Hick's law Huffman coding information bottleneck method information theoretic
Index of information theory articles
Index_of_information_theory_articles
Non-parametric statistic on information transfer
Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes
Transfer_entropy
Concept 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. Consider
Inequalities in information theory
Inequalities_in_information_theory
Measure of distinguishability between two quantum states
In quantum information theory, quantum relative entropy is a measure of distinguishability between two quantum states. It is the quantum mechanical analog
Quantum_relative_entropy
Interpretation of entropy as the change in arrangement of a system's particles
Entropy (information theory) Entropy (computing) Entropy (energy dispersal) Second law of thermodynamics Entropy (statistical thermodynamics) Entropy
Entropy_(order_and_disorder)
Information-theoretic measure
In information theory, the cross-entropy between two probability distributions p {\displaystyle p} and q {\displaystyle q} , over the same underlying
Cross-entropy
Computing concept
of 80 lava lamps as an additional source of entropy. Entropy (information theory) Entropy Randomness random(4) - Linux man page Archived 2007-10-11 at
Entropy_(computing)
Type of entropy in quantum theory
entropy from classical information theory. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is S = − tr ( ρ ln
Von_Neumann_entropy
Venn diagram to illustrate relationship
Shannon's basic measures of information: entropy, joint entropy, conditional entropy and mutual information. Information diagrams are a useful pedagogical tool
Information_diagram
Theory within consciousness research
Integrated information theory (IIT) proposes a mathematical model for the consciousness of a system. It comprises a framework ultimately intended to explain
Integrated_information_theory
Message encoded with more bits than needed
In information theory, redundancy (redundation) measures the fractional difference between the entropy H(X) of an ensemble X, and its maximum possible
Redundancy (information theory)
Redundancy_(information_theory)
Facts provided or learned about something or someone
representation, and entropy. Information is often processed iteratively: Data available at one step are processed into information to be interpreted and
Information
Physical lower limit to energy consumption of computation
limit Bekenstein bound Kolmogorov complexity Entropy in thermodynamics and information theory Information theory Jarzynski equality Limits of computation
Landauer's_principle
Subfield of information theory and computer science
the same inequalities (except for a constant) that entropy does, as in classical information theory; randomness is incompressibility; and, within the realm
Algorithmic information theory
Algorithmic_information_theory
Theory about lossy data compression
Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the
Rate–distortion_theory
Generalization of the standard Boltzmann–Gibbs entropy
identical in form to Havrda–Charvát structural α-entropy, introduced in 1967 within information theory. Given a discrete set of probabilities { p i } {\displaystyle
Tsallis_entropy
Quantity in information theory
In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of
Information_content
Classic entropy of a quantum-mechanical density matrix
In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type
Wehrl_entropy
Term in information theory
In information theory, information dimension is an information measure for random vectors in Euclidean space, based on the normalized entropy of finely
Information_dimension
Physical law for entropy and heat
first formulation, which preceded the proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist
Second_law_of_thermodynamics
ideas of the information entropy and redundancy of a source, and its relevance through the source coding theorem; the mutual information, and the channel
History_of_information_theory
Measurement scale based on orders of magnitude
semiring Preferred number Semi-log plot Order of magnitude Entropy Entropy (information theory) pH Richter magnitude scale "Slide Rule Sense: Amazonian
Logarithmic_scale
Relationship of various quantum subsystems
In quantum information theory, strong subadditivity of quantum entropy (SSA) is the relation among the von Neumann entropies of various quantum subsystems
Strong subadditivity of quantum entropy
Strong_subadditivity_of_quantum_entropy
Subject of study in ergodic theory
classified. Bernoulli shifts are classified by their metric entropy. See Ornstein theory for more. Krieger finite generator theorem (Krieger 1970)—Given
Measure-preserving dynamical system
Measure-preserving_dynamical_system
Measure of income inequality
The generalized entropy index has been proposed as a measure of income inequality in a population. It is derived from information theory as a measure of
Generalized_entropy_index
between information theory, inference and machine learning in his book. 2006 – Jarosław Duda introduces first Asymmetric numeral systems entropy coding:
Timeline of information theory
Timeline_of_information_theory
Spectral density estimation method
which corresponds to the concept of maximum entropy as used in both statistical mechanics and information theory, is maximally non-committal with regard to
Maximum entropy spectral estimation
Maximum_entropy_spectral_estimation
Influence of thermodynamics on evolution
relationship between entropy and living organisms have inspired hypotheses and speculations in many contexts, including psychology, information theory, the origin
Entropy_and_life
Measure of algorithmic complexity
algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory. The
Kolmogorov_complexity
Information-theoretic measure of complexity
Information fluctuation complexity is an information-theoretic quantity defined as the fluctuation of information about entropy. It is derivable from
Information fluctuation complexity
Information_fluctuation_complexity
Decision tree training concept
relative entropies subtracted from the total entropy are 0. The split information value for a test is defined as follows: SplitInformation ( X ) = −
Information_gain_ratio
Mathematical analysis of gambling
might be thought of as gambling theory applied to real-world events. The myriad applications for logarithmic information measures inform optimal decisions
Gambling and information theory
Gambling_and_information_theory
thermodynamic entropy is straightforward, but arbitrary and not immediately obvious to anyone unfamiliar with information theory. Missing information: The idea
Introduction_to_entropy
Measure of unpredictability of outcomes
The min-entropy, in information theory, is the smallest of the Rényi family of entropies, corresponding to the most conservative way of measuring the unpredictability
Min-entropy
Establishes the limits to possible data compression
per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost. However it is possible to
Shannon's source coding theorem
Shannon's_source_coding_theorem
Measure of relative information in quantum information theory
entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory.
Conditional_quantum_entropy
of the concepts in information theory have separate definitions and formulas for continuous and discrete cases. For example, entropy H ( X ) {\displaystyle
Information theory and measure theory
Information_theory_and_measure_theory
Partial Information Decomposition is an extension of information theory, that aims to generalize the pairwise relations described by information theory to
Partial information decomposition
Partial_information_decomposition
Concept in general relativity and quantum field theory
relates the entanglement entropy of a boundary conformal field theory to a specific surface in its dual gravitational theory. In the early 1990s Gerard
Black_hole_thermodynamics
Methods of estimating differential entropy given some observations
of information estimates. In Information Theory in Psychology: Problems and Methods, pp. 95–100. E. G. Learned-Miller (2003) A new class of entropy estimators
Entropy_estimation
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-entropy. The Hartley function
Hartley_function
Upper limit on entropy in physics
after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space
Bekenstein_bound
American mathematician (1916–2001)
IT: A Primer on Shannon's Entropy and Information", in Duplantier, Bertrand; Rivasseau, Vincent (eds.), Information Theory: Poincaré Seminar 2018, Progress
Claude_Shannon
In information theory, the graph entropy is a measure of the information rate achievable by communicating symbols over a channel in which certain pairs
Graph_entropy
Quantum information quantity
Reflected entropy is a quantity in quantum information theory that measures correlations in a bipartite quantum-mechanical system described by a mixed
Reflected_entropy
Measure of connection disorder in a network
the network entropy is a disorder measure derived from information theory to describe the level of randomness and the amount of information encoded in
Network_entropy
Austrian mathematician and theoretical physicist (1844–1906)
inscription of Boltzmann's entropy formula: S = k ⋅ log W {\displaystyle S=k\cdot \log W} . Boltzmann's kinetic theory of gases seemed to presuppose
Ludwig_Boltzmann
Academic journal
Entropy is a monthly open access scientific journal covering research on all aspects of entropy and information theory. It was established in 1999 and
Entropy_(journal)
Entropy measure
Coherent information is an entropy measure used in quantum information theory. It is a property of a quantum state ρ and a quantum channel N {\displaystyle
Coherent_information
Thought experiment of 1867
molecules without increasing entropy. However, due to the connection between entropy in thermodynamics and information theory, this also meant that the recorded
Maxwell's_demon
Topics referred to by the same term
computing the start and the remainder Chain rule for entropy (information theory), for the Shannon entropy of two consecutive experiments Reverse chain rule
Chain_rule_(disambiguation)
Puzzle of disappearance of information in a black hole
discussed above. The loss of information can be quantified in terms of the change in the fine-grained von Neumann entropy of the state. A pure state is
Black hole information paradox
Black_hole_information_paradox
Information theory
theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of
Conditional mutual information
Conditional_mutual_information
Concept in information theory
In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal
Entropic_uncertainty
Disorder analysis in sociocultural systems
entropy is a sociological theory that evaluates social behaviours using a method based on the second law of thermodynamics. The equivalent of entropy
Social_entropy
Generalization of the concept from statistical mechanics
partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of
Partition function (mathematics)
Partition_function_(mathematics)
Notion in information theory
In information theory, the limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy. It was formulated
Limiting density of discrete points
Limiting_density_of_discrete_points
Unit of information
In information theory, one bit is the information entropy of a random binary variable that is 0 or 1 with equal probability, or the information that
Bit
Use of the second law of thermodynamics to distinguish past from future
Entropy is one of the few quantities in the physical sciences that requires a particular direction for time, sometimes called an arrow of time. As one
Entropy_as_an_arrow_of_time
Measure of dependence
In information theory, dual total correlation, information rate, excess entropy, or binding information is one of several known non-negative generalizations
Dual_total_correlation
Measure of distance between two clusterings related to mutual information
In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings
Variation_of_information
mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information, where quantity
Quantities_of_information
1948 scholarly article by Claude Shannon
which the message is intended It also developed the concepts of information entropy, redundancy and the source coding theorem, and introduced the term
A Mathematical Theory of Communication
A_Mathematical_Theory_of_Communication
Theoretical Physics
posits a quantitative relationship between the entanglement entropy of a conformal field theory and the geometry of an associated anti-de Sitter spacetime
Ryu–Takayanagi_conjecture
Device or program that encodes/decodes audio data in some bitstream format
Vector Wavelet Daubechies DWT Theory Compressed data structures Compressed suffix array FM-index Entropy Information theory Timeline Kolmogorov complexity
Audio_codec
Concept in information theory
Look up perplexity in Wiktionary, the free dictionary. In information theory, perplexity is a measurement of how well a probability distribution or probability
Perplexity
Unit of information
The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information or information entropy, based on natural logarithms
Nat_(unit)
Unit of information
is a unit of information named after Claude Shannon, the founder of information theory. IEC 80000-13 defines the shannon as the information content associated
Shannon_(unit)
Number representing system complexity
In mathematics, the topological entropy of a topological dynamical system is a nonnegative extended real number that is a measure of the complexity of
Topological_entropy
or coauthored two textbooks on quantum information theory. The first textbook utilizes the von Neumann entropy and its variants and the notion of typical
Mark_Wilde
Psychological effect involving letters in a word
relative influences of the exterior and interior letters of words. Entropy (information theory) Unscrambled: "According to a recshearch [sic] at Cambridge University
Transposed_letter_effect
Observational basis of thermodynamics
define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium.
Laws_of_thermodynamics
entropic vector or entropic function is a concept arising in information theory. It represents the possible values of Shannon's information entropy that
Entropic_vector
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