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.