Entropy (information theory) Also known as: entropy · Shannon entropy · average information content · negentropy
Community · Entropy (information theory) 1 Quantifies the uncertainty associated with a random variable. 2 Measured in bits, nats, or bans. 3 Used to determine the theoretical limit for lossless data compression. 4 Analogous to thermodynamic entropy in physics. 5 Fundamental to the definition of channel capacity. Shannon entropy is a mathematical measure of the average amount of information produced by a stochastic source of data.
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Standard unit of information entropy
The bit serves as the fundamental unit of information when entropy is calculated using a base-2 logarithm, representing the uncertainty of a binary choice.
Foundational publication introducing the concept
This 1948 paper by Claude Shannon formally introduced entropy as a measure of information, establishing the mathematical framework for the field.
Primary developer of the concept
Claude Shannon formulated the definition of entropy in the context of information theory to quantify the information content of messages.
Entropy is a fundamental component of information theory.
Shannon entropy serves as the primary metric for quantifying information within the framework of information theory.
Constraint on reliable communication
This theorem defines the channel capacity, which is the maximum rate at which information can be transmitted over a noisy channel, limited by the entropy of the noise.
Practical application of entropy limits
Shannon's source coding theorem establishes that the entropy of a source sets a fundamental limit on the maximum lossless data compression achievable.
Conceptual precursor in statistical mechanics
Shannon's entropy formula is mathematically analogous to the Boltzmann entropy formula used in physics to describe the disorder of a system.
Institutional birthplace of the theory
Shannon developed the concept of information entropy while working as a researcher at Bell Labs in the 1940s.
Measure of shared information between variables
Derived from entropy, this quantity measures the amount of information obtained about one random variable through observing another.
Measure of difference between probability distributions
This metric quantifies how one probability distribution differs from a second, reference distribution, building directly upon the concept of Shannon entropy.
Principle for statistical inference
This principle states that the probability distribution which best represents the current state of knowledge is the one with the largest entropy.
In information theory, entropy serves as a quantitative measure of the average uncertainty or information content inherent in a random variable . It essentially calculates the expected amount of data required to describe the state of a variable based on its underlying probability distribution .
Entropy Η( X ) (i.e. the expected surprisal ) of a coin flip, measured in bits, graphed versus the bias of the coin Pr( X = 1), where X = 1 represents a result of heads. [ 10 ]: 14–15 Here, the entropy is at most 1 bit, and to communicate the outcome of a coin flip (2 possible values) will require an average of at mos... Wikimedia Commons: File:Binary_entropy_plot.svg The mathematical formulation involves a sum over all possible outcomes, weighted by their respective probabilities. The choice of the logarithm base determines the unit of measurement: base 2 yields bits , base e results in nats , and base 10 produces dits or hartleys . Fundamentally, entropy is equivalent to the expected value of a variable's self-information .
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