Boltzmann distribution
E46139
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Boltzmann distribution canonical | 8 |
| Boltzmann factor | 3 |
| Boltzmann statistics | 2 |
| Gibbs distribution | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T364198 — 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 distribution Context triple: [Boltzmann machines, basedOn, Boltzmann distribution]
-
A.
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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B.
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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C.
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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D.
Boltzmann constant
The Boltzmann constant is a fundamental physical constant that links temperature to energy at the particle level, playing a central role in statistical mechanics and thermodynamics.
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E.
Boltzmann–Gibbs entropy in statistical mechanics
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.
- 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 distribution Target entity description: The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
-
A.
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.
-
B.
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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C.
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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D.
Boltzmann constant
The Boltzmann constant is a fundamental physical constant that links temperature to energy at the particle level, playing a central role in statistical mechanics and thermodynamics.
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E.
Boltzmann–Gibbs entropy in statistical mechanics
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in statistical mechanics
ⓘ
probability distribution ⓘ |
| appliesTo | systems in thermal equilibrium ⓘ |
| approximationOf |
Bose–Einstein distribution at high temperature and low density
ⓘ
Fermi–Dirac distribution at high temperature and low density ⓘ |
| assumes | classical distinguishable particles in many applications ⓘ |
| contrastsWith |
Bose–Einstein statistics
ⓘ
surface form:
Bose–Einstein distribution
Fermi–Dirac statistics ⓘ
surface form:
Fermi–Dirac distribution
|
| dependsOn |
Boltzmann constant
ⓘ
energy of the state ⓘ temperature ⓘ |
| describes | probability of a system occupying a state with given energy at thermal equilibrium ⓘ |
| field |
physics
ⓘ
statistical mechanics ⓘ thermodynamics ⓘ |
| hasComponent | Boltzmann factor exp(-E/(k_B T)) ⓘ |
| hasMathematicalForm | P(E) ∝ exp(-E/(k_B T)) ⓘ |
| implies | higher energy states are less populated than lower energy states ⓘ |
| namedAfter | Ludwig Boltzmann ⓘ |
| normalizationCondition | sum over all states of P(E_i) = 1 ⓘ |
| relatedConcept |
Boltzmann–Gibbs entropy in statistical mechanics
ⓘ
surface form:
Boltzmann entropy formula
grand canonical ensemble ⓘ microcanonical ensemble ⓘ |
| relatedTo |
Boltzmann distribution
self-linksurface differs
ⓘ
surface form:
Boltzmann factor
Boltzmann distribution self-linksurface differs ⓘ
surface form:
Gibbs distribution
Maxwell–Boltzmann statistics ⓘ
surface form:
Maxwell–Boltzmann distribution
canonical ensemble ⓘ partition function ⓘ |
| temperatureEffect | higher temperature increases population of higher energy states ⓘ |
| usedFor |
calculating average energy
ⓘ
calculating entropy in canonical ensemble ⓘ calculating heat capacity ⓘ deriving macroscopic thermodynamic quantities ⓘ population of electronic energy levels ⓘ population of energy levels in gases ⓘ population of molecular rotational states ⓘ population of molecular vibrational states ⓘ |
| usedIn |
astrophysics
ⓘ
chemical equilibrium calculations ⓘ laser physics ⓘ molecular simulations ⓘ plasma physics ⓘ reaction rate theory ⓘ spectroscopy ⓘ |
| usesSymbol |
E for energy
ⓘ
T for absolute temperature ⓘ k_B for Boltzmann constant ⓘ |
| validWhen |
system is ergodic
ⓘ
system is in contact with a heat bath at fixed temperature ⓘ |
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 distribution Description of subject: The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
Referenced by (15)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Gibbs distribution
this entity surface form:
Boltzmann factor
this entity surface form:
Boltzmann statistics
this entity surface form:
Boltzmann statistics
subject surface form:
On Ionization in the Solar Chromosphere
this entity surface form:
Boltzmann factor
subject surface form:
Markov random field
this entity surface form:
Gibbs distribution
this entity surface form:
Boltzmann factor