Triple

T3677827
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Khinchin E78037 entity
Predicate notableWork P4 FINISHED
Object 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.
E378998 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: Mathematical Foundations of Statistical Mechanics | Statement: [Aleksandr Khinchin, notableWork, Mathematical Foundations of Statistical Mechanics]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mathematical Foundations of Statistical Mechanics
Context triple: [Aleksandr Khinchin, notableWork, Mathematical Foundations of Statistical Mechanics]
  • A. 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.
  • 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. Carathéodory’s formulation of the second law of thermodynamics
    Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.
  • D. 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.
  • E. Onsager reciprocal relations
    Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
  • 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: Mathematical Foundations of Statistical Mechanics
Triple: [Aleksandr Khinchin, notableWork, Mathematical Foundations of Statistical Mechanics]
Generated description
Mathematical Foundations of Statistical Mechanics is a classic monograph by Aleksandr Khinchin that rigorously develops the probabilistic and measure-theoretic underpinnings of statistical mechanics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mathematical Foundations of Statistical Mechanics
Target entity description: Mathematical Foundations of Statistical Mechanics is a classic monograph by Aleksandr Khinchin that rigorously develops the probabilistic and measure-theoretic underpinnings of statistical mechanics.
  • A. 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.
  • 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. Carathéodory’s formulation of the second law of thermodynamics
    Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.
  • D. 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.
  • E. Onsager reciprocal relations
    Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
  • 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_69ad85e18c1c8190be8aafb227f39f48 completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adc4643cf08190b2d10ddf4aac7407 completed March 8, 2026, 6:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4c3a50d40819081aad0c72bcaee9d completed March 14, 2026, 2:10 a.m.
NEDg Description generation batch_69b4c451a5048190bfd4675cd17de655 completed March 14, 2026, 2:13 a.m.
NED2 Entity disambiguation (via description) batch_69b4c494ad80819084d6aa10fe62a63b completed March 14, 2026, 2:14 a.m.
Created at: March 8, 2026, 3:25 p.m.