Information Theory and Statistical Mechanics.¶
Jaynes, E. T. (1957). Information Theory and Statistical Mechanics. Physical Review, 106(4), 620-630.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Degrees of Freedom
- In information and machine learning contexts, Jaynes' maximum-entropy principle
This sourceDerives the canonical (and other) ensembles as maximum-entropy distributions subject to constraints on known observables; supplies the information-theoretic principle that the fewest DOFs consistent with the constraints minimize model complexity.
Supported in partVerified against the publisher's abstract
Jaynes 1957 states the maximum-entropy principle for inference from partial information, but does not mention machine learning or the selection of essential degrees of freedom.
“Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information.”
- In information and machine learning contexts, Jaynes' maximum-entropy principle
- Ensemble
- The information-theoretic foundation for ensemble derivation comes from Jaynes
This sourceDerives canonical and other ensembles as maximum-entropy distributions subject to constraints on known observables, grounding ensembles as a consequence of inference under partial information.
Supported in partVerified against the publisher's abstract
Jaynes's abstract states that information theory yields the maximum-entropy estimate from partial knowledge and that the partition-function rules follow, but it does not itself mention ensembles.
“Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate.”
- The information-theoretic foundation for ensemble derivation comes from Jaynes
- Entropy (Thermodynamic Sense)
- ) and Jaynes (1957
This sourceDerives the canonical (and other) ensembles as maximum-entropy distributions subject to constraints; establishes the information-theoretic foundation linking Shannon and Gibbs/Boltzmann entropy.
SupportedVerified against the publisher's abstract
Jaynes presents information theory as supplying "a constructive criterion for setting up probability distributions on the basis of partial knowledge", yielding an estimate that is "maximally noncommittal with regard to missing information". Treating statistical mechanics as a form of statistical inference, he finds that the usual computational rules "are an immediate consequence of the maximum-entropy principle". That is the principle the sentence names, joining information-theoretic inference to the machinery of statistical mechanics. The work supplies the maximum-entropy principle itself, not the historical attributions to Clausius, Boltzmann, Gibbs and Shannon or the entropy formula that surround the sentence.
“Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate.”
- ) and Jaynes (1957
Domain-specific¶
- Maximum entropy thermodynamics
- Principle of Maximum Entropy
- With informative constraints, the selected distribution can be sharply nonuniform.
This sourceThe accessible abstract states the partial-knowledge probability-assignment criterion and its statistical-mechanics application.
- With informative constraints, the selected distribution can be sharply nonuniform.
Verification¶
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Links previously used in the corpus¶
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