Triple

T10084784
Position Surface form Disambiguated ID Type / Status
Subject Joseph Edward Mayer E215191 entity
Predicate notableWork P4 FINISHED
Object Mayer cluster expansion in statistical mechanics
The Mayer cluster expansion in statistical mechanics is a mathematical method that expresses the thermodynamic properties of interacting particle systems as a series in terms of cluster integrals, enabling systematic analysis of non-ideal gases and liquids.
E841011 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: Mayer cluster expansion in statistical mechanics | Statement: [Joseph Edward Mayer, notableWork, Mayer cluster expansion in statistical mechanics]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mayer cluster expansion in statistical mechanics
Context triple: [Joseph Edward Mayer, notableWork, Mayer cluster 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. Boltzmann–Gibbs entropy in statistical mechanics
    Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
  • C. Ehrenfest classification of phase transitions
    The Ehrenfest classification of phase transitions is an early theoretical scheme that categorizes phase transitions by the order of discontinuity in thermodynamic derivatives, such as entropy or specific heat, at the transition point.
  • D. Mathematical Foundations of Statistical Mechanics
    Mathematical Foundations of Statistical Mechanics is a classic monograph by Aleksandr Khinchin that rigorously develops the probabilistic and measure-theoretic underpinnings of statistical mechanics.
  • E. The Principles of Statistical Mechanics
    The Principles of Statistical Mechanics is a classic 1938 textbook by Richard C. Tolman that systematically develops the foundations of statistical mechanics and its applications to thermodynamics and physical chemistry.
  • 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: Mayer cluster expansion in statistical mechanics
Triple: [Joseph Edward Mayer, notableWork, Mayer cluster expansion in statistical mechanics]
Generated description
The Mayer cluster expansion in statistical mechanics is a mathematical method that expresses the thermodynamic properties of interacting particle systems as a series in terms of cluster integrals, enabling systematic analysis of non-ideal gases and liquids.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mayer cluster expansion in statistical mechanics
Target entity description: The Mayer cluster expansion in statistical mechanics is a mathematical method that expresses the thermodynamic properties of interacting particle systems as a series in terms of cluster integrals, enabling systematic analysis of non-ideal gases and liquids.
  • 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. Boltzmann–Gibbs entropy in statistical mechanics
    Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
  • C. Ehrenfest classification of phase transitions
    The Ehrenfest classification of phase transitions is an early theoretical scheme that categorizes phase transitions by the order of discontinuity in thermodynamic derivatives, such as entropy or specific heat, at the transition point.
  • D. Mathematical Foundations of Statistical Mechanics
    Mathematical Foundations of Statistical Mechanics is a classic monograph by Aleksandr Khinchin that rigorously develops the probabilistic and measure-theoretic underpinnings of statistical mechanics.
  • E. The Principles of Statistical Mechanics
    The Principles of Statistical Mechanics is a classic 1938 textbook by Richard C. Tolman that systematically develops the foundations of statistical mechanics and its applications to thermodynamics and physical chemistry.
  • 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_69ca83a1eed081908b2e9580f2ebeea7 completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cdd044c1ec8190b5b48cdb0584d00c completed April 2, 2026, 2:11 a.m.
NED1 Entity disambiguation (via context triple) batch_69d2b68188c48190ac783cdfc072c502 completed April 5, 2026, 7:22 p.m.
NEDg Description generation batch_69d2b7aecdb081909f651c1bc1bcfd75 completed April 5, 2026, 7:27 p.m.
NED2 Entity disambiguation (via description) batch_69d2b86bf8948190a79046efadc4adea completed April 5, 2026, 7:30 p.m.
Created at: March 30, 2026, 9 p.m.