virial theorem
E290121
The virial theorem is a fundamental result in mechanics and astrophysics that relates the average kinetic and potential energies of a bound system in equilibrium, widely used to study the stability and dynamics of stars, galaxies, and gas clouds.
All labels observed (5)
| Label | Occurrences |
|---|---|
| quantum mechanical virial theorem | 1 |
| relativistic virial theorem | 1 |
| scalar virial theorem | 1 |
| tensor virial theorem | 1 |
| virial theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2707263 — 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: virial theorem Context triple: [Jeans mass, relatedTo, virial theorem]
-
A.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
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B.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
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C.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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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.
equipartition theorem
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.
- 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: virial theorem Target entity description: The virial theorem is a fundamental result in mechanics and astrophysics that relates the average kinetic and potential energies of a bound system in equilibrium, widely used to study the stability and dynamics of stars, galaxies, and gas clouds.
-
A.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
-
B.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
-
C.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
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.
equipartition theorem
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.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
result in astrophysics
ⓘ
result in classical mechanics ⓘ theorem ⓘ |
| appliesTo |
bound systems
ⓘ
molecular systems in statistical mechanics ⓘ self-gravitating systems ⓘ systems in equilibrium ⓘ systems with power-law potentials ⓘ |
| assumes |
bound or confined motion
ⓘ
time averages over long timescales ⓘ |
| coreStatement | for a stable, bound system with potential energy proportional to r^n, 2⟨T⟩ = n⟨V⟩ ⓘ |
| field |
astrophysics
ⓘ
dynamical astronomy ⓘ mechanics ⓘ statistical mechanics ⓘ |
| generalizes | to systems with time-averaged equilibrium ⓘ |
| hasFormulation |
virial theorem
self-linksurface differs
ⓘ
surface form:
quantum mechanical virial theorem
virial theorem self-linksurface differs ⓘ
surface form:
relativistic virial theorem
virial theorem self-linksurface differs ⓘ
surface form:
scalar virial theorem
virial theorem self-linksurface differs ⓘ
surface form:
tensor virial theorem
|
| historicalOrigin | developed by Rudolf Clausius ⓘ |
| mathematicalTool | time averaging of dynamical quantities ⓘ |
| nameOrigin | derived from the Latin word 'vis' meaning force or energy ⓘ |
| relatedTo |
Jeans instability
ⓘ
Jeans theorem ⓘ equipartition of energy ⓘ gravitational binding energy ⓘ hydrostatic equilibrium ⓘ virial equilibrium ⓘ virial parameter ⓘ |
| relates |
average kinetic energy
ⓘ
average potential energy ⓘ |
| specialCase | for inverse-square law forces, 2⟨T⟩ = -⟨V⟩ ⓘ |
| usedFor |
analyzing dynamical equilibrium of galaxy clusters
ⓘ
analyzing hydrostatic equilibrium of stars ⓘ constraining dark matter content of clusters ⓘ deriving Jeans instability criterion (via energy arguments) ⓘ deriving conditions for gravitational collapse ⓘ deriving virial mass of dark matter halos ⓘ estimating binding energy of self-gravitating systems ⓘ estimating masses of astronomical systems ⓘ estimating temperature of self-gravitating gas ⓘ estimating total mass of galaxy clusters ⓘ relating velocity dispersion to mass in galaxies ⓘ studying stability of galaxies ⓘ studying stability of molecular clouds ⓘ studying stability of star clusters ⓘ studying stability of stars ⓘ testing N-body simulations in astrophysics ⓘ |
| yearProposed | 1870 ⓘ |
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: virial theorem Description of subject: The virial theorem is a fundamental result in mechanics and astrophysics that relates the average kinetic and potential energies of a bound system in equilibrium, widely used to study the stability and dynamics of stars, galaxies, and gas clouds.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
scalar virial theorem
this entity surface form:
tensor virial theorem
this entity surface form:
quantum mechanical virial theorem
this entity surface form:
relativistic virial theorem