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.
Aliases (2)
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 → |
Referenced by (8)
| Subject (surface form when different) | Predicate |
|---|---|
|
Constantino Tsallis
→
Constantino Tsallis ("Tsallis statistics") → |
hasConceptNamedAfter |
|
Rényi entropy
→
Shannon–Khinchin axioms → |
relatedTo |
|
Boltzmann–Gibbs entropy
→
|
contrastedWith |
|
Shannon entropy
→
|
isSpecialCaseOf |
|
Constantino Tsallis
→
|
knownFor |
|
Constantino Tsallis
("q-Gaussian distribution")
→
|
notableConcept |