Triple
T2093723
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arnold Sommerfeld |
E32730
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Sommerfeld expansion in statistical mechanics
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.
|
E234761
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Sommerfeld expansion in statistical mechanics | Statement: [Arnold Sommerfeld, knownFor, Sommerfeld expansion in statistical mechanics]
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]
-
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.
-
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.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Sommerfeld expansion in statistical mechanics Triple: [Arnold Sommerfeld, knownFor, Sommerfeld expansion in statistical mechanics]
Generated 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.
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.
-
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
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69a885eba0708190999696a45cbec816 |
completed | March 4, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69abba98c32081908a243bc7088a1510 |
completed | March 7, 2026, 5:41 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ae305aacc08190904a358fc4207075 |
completed | March 9, 2026, 2:28 a.m. |
| NEDg | Description generation | batch_69ae30e0411c81908cd19bf8d3525056 |
completed | March 9, 2026, 2:30 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ae31871d408190a4ae64372660fa79 |
completed | March 9, 2026, 2:33 a.m. |
Created at: March 4, 2026, 7:43 p.m.