Maxwell–Boltzmann statistics
E7350
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.
All labels observed (5)
How this entity was disambiguated
This entity first appeared as the object of triple T79839 — 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: Maxwell–Boltzmann statistics Context triple: [Bose–Einstein statistics, contrastsWith, Maxwell–Boltzmann statistics]
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A.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
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B.
Fermi–Dirac statistics
Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
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C.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
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D.
Planck radiation law
Planck radiation law is a fundamental formula in quantum physics that describes the spectral distribution of electromagnetic radiation emitted by a black body in thermal equilibrium.
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E.
Einstein coefficients
Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
- 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: Maxwell–Boltzmann statistics Target entity description: 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.
-
A.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
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B.
Fermi–Dirac statistics
Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
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C.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
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D.
Planck radiation law
Planck radiation law is a fundamental formula in quantum physics that describes the spectral distribution of electromagnetic radiation emitted by a black body in thermal equilibrium.
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E.
Einstein coefficients
Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
classical statistics
ⓘ
physical theory ⓘ statistical theory ⓘ |
| appliesTo |
classical particles
ⓘ
distinguishable particles ⓘ ideal gas ⓘ non-quantum particles ⓘ |
| assumes |
Boltzmann counting of microstates
ⓘ
classical limit ⓘ dilute gas ⓘ distinguishability of particles ⓘ no quantum degeneracy ⓘ non-interacting particles ⓘ thermal equilibrium ⓘ |
| basedOn |
Boltzmann–Gibbs entropy in statistical mechanics
ⓘ
surface form:
Boltzmann entropy formula
classical phase space ⓘ |
| breaksDownWhen |
particles are indistinguishable quantum mechanically
ⓘ
quantum effects are significant ⓘ |
| category |
classical statistical mechanics
ⓘ
probability distributions in physics ⓘ |
| contrastsWith |
Bose–Einstein statistics
ⓘ
Fermi–Dirac statistics ⓘ |
| dependsOn |
Boltzmann constant
ⓘ
absolute temperature ⓘ |
| describes |
distribution of particle energies
ⓘ
distribution of particle speeds ⓘ equilibrium properties of gases ⓘ mean speed of gas molecules ⓘ most probable speed of gas molecules ⓘ root-mean-square speed of gas molecules ⓘ |
| developedBy |
James Clerk Maxwell
ⓘ
Ludwig Boltzmann ⓘ |
| field |
statistical mechanics
ⓘ
thermodynamics ⓘ |
| historicalPeriod | 19th century physics ⓘ |
| mathematicalForm | exponential of negative energy over kT ⓘ |
| relatedTo |
Boltzmann distribution
ⓘ
Maxwell–Boltzmann statistics self-linksurface differs ⓘ
surface form:
Maxwell–Boltzmann distribution
equipartition theorem ⓘ kinetic theory of gases ⓘ partition function ⓘ |
| usedFor |
calculating transport coefficients
ⓘ
deriving ideal gas law ⓘ modeling classical plasmas ⓘ modeling dilute molecular gases ⓘ |
| validWhen |
high temperature limit
ⓘ
low particle density ⓘ |
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: Maxwell–Boltzmann statistics Description of subject: 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.
Referenced by (18)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution precursor
this entity surface form:
Maxwell–Boltzmann distribution
subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
equilibrium Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann distribution
this entity surface form:
Maxwell–Boltzmann speed distribution
this entity surface form:
Maxwell–Boltzmann distribution