equipartition theorem
E57415
The equipartition theorem is a principle in classical statistical mechanics stating that, at thermal equilibrium, each independent quadratic degree of freedom of a system contributes an average energy of (1/2)kT.
All labels observed (2)
| Label | Occurrences |
|---|---|
| equipartition theorem canonical | 4 |
| classical equipartition theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T461612 — 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: equipartition theorem Context triple: [Maxwell–Boltzmann statistics, relatedTo, equipartition theorem]
-
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.
Boltzmann distribution
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.
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C.
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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D.
Boltzmann equation
The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.
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E.
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.
- 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: equipartition theorem Target entity description: The equipartition theorem is a principle in classical statistical mechanics stating that, at thermal equilibrium, each independent quadratic degree of freedom of a system contributes an average energy of (1/2)kT.
-
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.
Boltzmann distribution
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.
-
C.
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.
-
D.
Boltzmann equation
The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.
-
E.
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.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
result in classical thermodynamics ⓘ theorem in statistical mechanics ⓘ |
| appliesTo |
classical systems
ⓘ
harmonic oscillator ⓘ ideal gas ⓘ molecules in a gas ⓘ solids in the classical limit ⓘ systems in thermal equilibrium ⓘ |
| assumes |
classical limit
ⓘ
continuous energy spectrum ⓘ thermal equilibrium ⓘ validity of classical mechanics ⓘ |
| concerns |
average energy
ⓘ
distribution of energy among degrees of freedom ⓘ thermal equilibrium properties ⓘ |
| contrastsWith | quantum statistics ⓘ |
| energyPerDegreeOfFreedom | (1/2)kT ⓘ |
| field |
classical mechanics
ⓘ
statistical mechanics ⓘ thermodynamics ⓘ |
| hasLimitation |
does not hold when energy levels are quantized and not thermally accessible
ⓘ
fails at low temperatures due to quantum effects ⓘ overestimates heat capacities of diatomic gases at room temperature ⓘ overestimates heat capacity of solids at low temperature ⓘ |
| historicallyAttributedTo |
James Clerk Maxwell
ⓘ
Ludwig Boltzmann ⓘ |
| implies |
Dulong–Petit law for molar heat capacity of many solids at high temperature
ⓘ
average translational kinetic energy per particle is (3/2)kT in three dimensions ⓘ each quadratic term in the Hamiltonian contributes (1/2)kT to the mean energy ⓘ heat capacity of a monatomic ideal gas is (3/2)Nk ⓘ internal energy of a monatomic ideal gas is (3/2)NkT ⓘ |
| mathematicallyBasedOn |
canonical ensemble average
ⓘ
classical Hamiltonian mechanics ⓘ phase space integrals ⓘ |
| relatedTo |
Boltzmann distribution
ⓘ
Dulong–Petit law ⓘ Maxwell–Boltzmann statistics ⓘ canonical ensemble ⓘ kinetic theory of gases ⓘ partition function ⓘ specific heat of gases ⓘ |
| statedAs | each independent quadratic degree of freedom contributes an average energy of (1/2)kT ⓘ |
| usedFor |
approximating high-temperature behavior of solids
ⓘ
deriving ideal gas internal energy ⓘ estimating heat capacities ⓘ understanding molecular motion ⓘ |
| usesQuantity |
Boltzmann constant
ⓘ
absolute temperature ⓘ degree of freedom ⓘ |
| validWhen | kT is large compared to energy level spacings ⓘ |
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: equipartition theorem Description of subject: The equipartition theorem is a principle in classical statistical mechanics stating that, at thermal equilibrium, each independent quadratic degree of freedom of a system contributes an average energy of (1/2)kT.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
Dulong–Petit law for molar heat capacity of many solids at high temperature
→
basedOn
→
classical equipartition theorem
ⓘ
linked to: equipartition theorem