Triple
T9756447
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Boltzmann–BGK equation |
E236564
|
entity |
| Predicate | relatesTo |
P37
|
FINISHED |
| Object |
Chapman–Enskog expansion
The Chapman–Enskog expansion is a systematic perturbative method in kinetic theory used to derive macroscopic fluid-dynamic equations, such as the Navier–Stokes equations, from the Boltzmann equation.
|
E46431
|
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: Chapman–Enskog expansion | Statement: [Boltzmann–BGK equation, relatesTo, Chapman–Enskog expansion]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chapman–Enskog expansion Context triple: [Boltzmann–BGK equation, relatesTo, Chapman–Enskog expansion]
-
A.
Boltzmann–BGK equation
The Boltzmann–BGK equation is a simplified kinetic model that replaces the complex collision term of the Boltzmann equation with a single relaxation-time approximation to describe gas particle dynamics.
-
B.
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.
-
C.
Boltzmann–Kac equation
The Boltzmann–Kac equation is a kinetic equation in statistical mechanics that models the evolution of the velocity distribution of particles in a gas, providing a probabilistic framework related to the classical Boltzmann equation.
-
D.
Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy
The Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy is a set of coupled equations in statistical mechanics that describes the time evolution of reduced distribution functions for many-particle systems.
-
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: Chapman–Enskog expansion Triple: [Boltzmann–BGK equation, relatesTo, Chapman–Enskog expansion]
Generated description
The Chapman–Enskog expansion is a systematic perturbative method in kinetic theory used to derive macroscopic fluid-dynamic equations, such as the Navier–Stokes equations, from the Boltzmann equation.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chapman–Enskog expansion Target entity description: The Chapman–Enskog expansion is a systematic perturbative method in kinetic theory used to derive macroscopic fluid-dynamic equations, such as the Navier–Stokes equations, from the Boltzmann equation.
-
A.
Boltzmann–BGK equation
The Boltzmann–BGK equation is a simplified kinetic model that replaces the complex collision term of the Boltzmann equation with a single relaxation-time approximation to describe gas particle dynamics.
-
B.
Boltzmann equation
chosen
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.
-
C.
Boltzmann–Kac equation
The Boltzmann–Kac equation is a kinetic equation in statistical mechanics that models the evolution of the velocity distribution of particles in a gas, providing a probabilistic framework related to the classical Boltzmann equation.
-
D.
Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy
The Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy is a set of coupled equations in statistical mechanics that describes the time evolution of reduced distribution functions for many-particle systems.
-
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.
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_69ca84d4eddc8190996fec1417d2bae8 |
completed | March 30, 2026, 2:12 p.m. |
| NER | Named-entity recognition | batch_69cd9fb2889481908fba4a449d5007fe |
completed | April 1, 2026, 10:44 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d1b02ff0f4819080410d4e7e809a24 |
completed | April 5, 2026, 12:43 a.m. |
| NEDg | Description generation | batch_69d1b1b8c75481909b847591b80255bc |
completed | April 5, 2026, 12:50 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d1b24f4af4819089b7e5b2b0165808 |
completed | April 5, 2026, 12:52 a.m. |
Created at: March 30, 2026, 8:24 p.m.