Tsallis entropy
E7558
concept in information theory
concept in statistical mechanics
entropy measure
generalized entropy
nonadditive entropy
Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Tsallis entropy canonical | 8 |
| Tsallis statistics | 3 |
| Possible generalization of Boltzmann–Gibbs statistics | 1 |
| q-Gaussian distribution | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T59017 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Tsallis entropy Context triple: [Shannon entropy, isSpecialCaseOf, Tsallis entropy]
-
A.
Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
-
B.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
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C.
Bekenstein–Hawking entropy
Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
-
D.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
E.
Maxwell–Boltzmann statistics
Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Tsallis entropy Target entity description: Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
-
A.
Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
-
B.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
-
C.
Bekenstein–Hawking entropy
Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
-
D.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
E.
Maxwell–Boltzmann statistics
Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in information theory
ⓘ
concept in statistical mechanics ⓘ entropy measure ⓘ generalized entropy ⓘ nonadditive entropy ⓘ |
| aimsToDescribe |
systems far from equilibrium
ⓘ
systems with power-law distributions ⓘ |
| appliesTo |
complex systems
ⓘ
multifractal systems ⓘ nonextensive systems ⓘ systems with long-range interactions ⓘ systems with long-term memory ⓘ |
| category |
information-theoretic measure
ⓘ
statistical physics concept ⓘ |
| characteristic |
nonadditivity
ⓘ
q-parameter dependence ⓘ |
| contrastWith | Boltzmann–Gibbs entropy ⓘ |
| domain | probability distributions ⓘ |
| field |
information theory
ⓘ
statistical mechanics ⓘ thermodynamics of complex systems ⓘ |
| generalizes | Shannon entropy ⓘ |
| hasMathematicalForm | S_q = (1 - \sum_i p_i^q) / (q - 1) ⓘ |
| hasParameter | entropic index q ⓘ |
| introducedBy | Constantino Tsallis ⓘ |
| introducedIn | 1988 ⓘ |
| motivatedBy | limitations of Boltzmann–Gibbs statistics for complex systems ⓘ |
| namedAfter | Constantino Tsallis ⓘ |
| property |
Lesche-stable for certain q ranges
ⓘ
concave for appropriate q ranges ⓘ |
| publishedIn | Journal of Statistical Physics ⓘ |
| reducesTo | Shannon entropy when q → 1 ⓘ |
| relatedConcept |
Rényi entropy
ⓘ
nonextensive statistical mechanics ⓘ q-Gaussian distribution ⓘ q-exponential distribution ⓘ |
| satisfies | generalized H-theorem in nonextensive framework ⓘ |
| usedFor |
maximum entropy principle with q-constraints
ⓘ
modeling heavy-tailed distributions ⓘ robust statistics in presence of outliers ⓘ |
| usedIn |
anomalous diffusion modeling
ⓘ
complex networks analysis ⓘ econophysics ⓘ generalized thermostatistics ⓘ image processing ⓘ machine learning ⓘ nonextensive statistical mechanics ⓘ turbulence studies ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Tsallis entropy Description of subject: Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
Referenced by (13)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
q-Gaussian distribution
this entity surface form:
Tsallis statistics
subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Possible generalization of Boltzmann–Gibbs statistics
this entity surface form:
Tsallis statistics