Sommerfeld expansion in statistical mechanics
E234761
The Sommerfeld expansion in statistical mechanics is an asymptotic method used to approximate integrals involving Fermi–Dirac distributions at low temperatures, widely applied to calculate thermodynamic properties of degenerate electron gases in metals.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Sommerfeld expansion in statistical mechanics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2093723 — 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: Sommerfeld expansion in statistical mechanics Context triple: [Arnold Sommerfeld, knownFor, Sommerfeld expansion in statistical mechanics]
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A.
Kirkwood approximation in statistical mechanics
The Kirkwood approximation in statistical mechanics is a method for approximating many-particle correlation functions by expressing higher-order correlations in terms of lower-order ones, simplifying the description of interacting particle systems.
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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.
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.
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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E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- 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: Sommerfeld expansion in statistical mechanics Target entity description: The Sommerfeld expansion in statistical mechanics is an asymptotic method used to approximate integrals involving Fermi–Dirac distributions at low temperatures, widely applied to calculate thermodynamic properties of degenerate electron gases in metals.
-
A.
Kirkwood approximation in statistical mechanics
The Kirkwood approximation in statistical mechanics is a method for approximating many-particle correlation functions by expressing higher-order correlations in terms of lower-order ones, simplifying the description of interacting particle systems.
-
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.
-
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.
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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E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
approximation method
ⓘ
asymptotic expansion method ⓘ mathematical technique in physics ⓘ |
| appliesTo |
Fermi–Dirac statistics
ⓘ
surface form:
Fermi–Dirac distribution
degenerate Fermi gas ⓘ electron gas in metals ⓘ low-temperature electron systems ⓘ |
| assumes |
smoothness of the function g(ε)
ⓘ
temperature much smaller than Fermi temperature ⓘ well-defined Fermi energy ⓘ |
| basedOn |
asymptotic expansion in powers of (k_B T)
ⓘ
expansion around the chemical potential ⓘ |
| category |
asymptotic analysis
ⓘ
low-temperature approximation techniques ⓘ methods in quantum statistics ⓘ |
| contrastsWith | high-temperature expansions of Fermi–Dirac integrals ⓘ |
| field | statistical mechanics ⓘ |
| gives |
higher-order corrections proportional to T^4, T^6, …
ⓘ
leading corrections proportional to T^2 ⓘ series in even powers of temperature ⓘ |
| mathematicalForm | integral expressed as series involving derivatives of g(ε) at ε = μ ⓘ |
| namedAfter | Arnold Sommerfeld ⓘ |
| relatedTo |
Fermi energy
ⓘ
chemical potential ⓘ degenerate electron gas ⓘ free-electron model ⓘ low-temperature thermodynamics ⓘ |
| requires | knowledge of derivatives of the density of states at the Fermi level ⓘ |
| typicalApplication |
calculation of low-temperature corrections to Fermi gas energy
ⓘ
derivation of linear-in-T electronic specific heat in metals ⓘ evaluation of carrier density at low temperature ⓘ |
| usedFor |
approximating integrals involving Fermi–Dirac distributions
ⓘ
calculating thermodynamic properties of degenerate electron gases ⓘ evaluating integrals of the form ∫ g(ε) f_FD(ε) dε ⓘ low-temperature expansions of Fermi systems ⓘ |
| usedIn |
Fermi liquid theory
ⓘ
calculation of electronic contribution to entropy ⓘ calculation of electronic contribution to internal energy ⓘ calculation of electronic contribution to pressure ⓘ calculation of electronic specific heat ⓘ condensed matter physics ⓘ free-electron model of metals ⓘ low-temperature transport theory of electrons ⓘ solid-state physics ⓘ theory of metals ⓘ |
| validWhen |
k_B T ≪ μ
ⓘ
system is strongly degenerate ⓘ |
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: Sommerfeld expansion in statistical mechanics Description of subject: The Sommerfeld expansion in statistical mechanics is an asymptotic method used to approximate integrals involving Fermi–Dirac distributions at low temperatures, widely applied to calculate thermodynamic properties of degenerate electron gases in metals.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.