Boltzmann–Gibbs entropy in statistical mechanics
E45253
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Boltzmann entropy | 7 |
| Boltzmann entropy formula | 4 |
| Gibbs entropy | 4 |
| Boltzmann–Gibbs entropy in statistical mechanics canonical | 1 |
| Boltzmann–Gibbs statistical mechanics | 1 |
| Gibbs paradox | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T356724 — 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: Boltzmann–Gibbs entropy in statistical mechanics Context triple: [Shannon–Khinchin axioms, characterizes, Boltzmann–Gibbs entropy in statistical mechanics]
-
A.
Tsallis 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.
-
B.
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.
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C.
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.
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D.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
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E.
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.
- 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: Boltzmann–Gibbs entropy in statistical mechanics Target entity description: Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
-
A.
Tsallis 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.
-
B.
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.
-
C.
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.
-
D.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
information measure
ⓘ
statistical mechanical entropy ⓘ thermodynamic entropy ⓘ |
| additivityProperty | additive for statistically independent subsystems ⓘ |
| appearsOn | Boltzmann’s tombstone formula S = k_B ln W ⓘ |
| appliesTo |
canonical ensemble
ⓘ
classical systems in equilibrium ⓘ grand canonical ensemble ⓘ microcanonical ensemble ⓘ |
| assumes |
ergodic hypothesis
ⓘ
short-range interactions in typical applications ⓘ |
| basisOf | classical equilibrium statistical mechanics ⓘ |
| concavityProperty | concave functional of the probability distribution ⓘ |
| continuousVersionName |
Boltzmann–Gibbs entropy in statistical mechanics
self-linksurface differs
ⓘ
surface form:
Gibbs entropy
|
| contrastedWith |
Rényi entropy
ⓘ
Tsallis entropy ⓘ |
| domain |
continuous probability densities
ⓘ
discrete probability distributions ⓘ |
| field |
information theory
ⓘ
statistical mechanics ⓘ thermodynamics ⓘ |
| historicalOrigin | late 19th century ⓘ |
| increasesWith | irreversible processes ⓘ |
| maximizationYields | Boltzmann distribution ⓘ |
| maximizedUnder |
constraints on average energy
ⓘ
normalization of probabilities ⓘ |
| monotonicWith | number of accessible microstates ⓘ |
| namedAfter |
Josiah Willard Gibbs
ⓘ
Ludwig Boltzmann ⓘ |
| quantifies |
disorder
ⓘ
number of microscopic configurations compatible with a macroscopic state ⓘ uncertainty ⓘ |
| relatedTo |
Boltzmann–Gibbs entropy in statistical mechanics
self-linksurface differs
ⓘ
surface form:
Boltzmann entropy
Boltzmann–Gibbs entropy in statistical mechanics self-linksurface differs ⓘ
surface form:
Gibbs entropy
H-theorem ⓘ Maxwell–Boltzmann statistics ⓘ
surface form:
Maxwell–Boltzmann distribution
Shannon entropy ⓘ canonical partition function ⓘ second law of thermodynamics ⓘ |
| standardFormula |
S = -k_B \sum_i p_i \ln p_i
ⓘ
S = k_B \ln W ⓘ |
| symbol | S ⓘ |
| unit | joule per kelvin ⓘ |
| usedFor |
characterizing equilibrium states
ⓘ
defining free energy ⓘ defining temperature in statistical mechanics ⓘ deriving thermodynamic relations ⓘ |
| usesConstant | Boltzmann constant ⓘ |
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: Boltzmann–Gibbs entropy in statistical mechanics Description of subject: Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
Referenced by (18)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Boltzmann entropy
this entity surface form:
Boltzmann entropy formula
this entity surface form:
Boltzmann entropy formula
Maxwell's demon thought experiment
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relatedConcept
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Boltzmann–Gibbs entropy in statistical mechanics
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this entity surface form:
Boltzmann entropy
Boltzmann–Gibbs entropy in statistical mechanics
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relatedTo
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Boltzmann–Gibbs entropy in statistical mechanics
self-linksurface differs
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subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Gibbs entropy
Boltzmann–Gibbs entropy in statistical mechanics
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relatedTo
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Boltzmann–Gibbs entropy in statistical mechanics
self-linksurface differs
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subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Boltzmann entropy
Boltzmann–Gibbs entropy in statistical mechanics
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continuousVersionName
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Boltzmann–Gibbs entropy in statistical mechanics
self-linksurface differs
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subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Gibbs entropy
this entity surface form:
Boltzmann entropy
this entity surface form:
Boltzmann entropy formula
this entity surface form:
Gibbs paradox
this entity surface form:
Boltzmann entropy formula
this entity surface form:
Gibbs entropy
this entity surface form:
Boltzmann entropy
this entity surface form:
Boltzmann–Gibbs statistical mechanics
this entity surface form:
Boltzmann entropy
Mathematical Foundations of Statistical Mechanics
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relatedTo
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Boltzmann–Gibbs entropy in statistical mechanics
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this entity surface form:
Boltzmann entropy
Mathematical Foundations of Statistical Mechanics
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relatedTo
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Boltzmann–Gibbs entropy in statistical mechanics
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this entity surface form:
Gibbs entropy