Triple

T7145249
Position Surface form Disambiguated ID Type / Status
Subject Bloch equations E166545 entity
Predicate relatedTo P37 FINISHED
Object Liouville–von Neumann equation
The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
E645944 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: Liouville–von Neumann equation | Statement: [Bloch equations, relatedTo, Liouville–von Neumann equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Liouville–von Neumann equation
Context triple: [Bloch equations, relatedTo, Liouville–von Neumann equation]
  • A. Schrödinger equation
    The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
  • B. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • C. Chapman–Kolmogorov equation
    The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
  • D. Tomonaga–Schwinger equation
    The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
  • E. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • 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: Liouville–von Neumann equation
Triple: [Bloch equations, relatedTo, Liouville–von Neumann equation]
Generated description
The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Liouville–von Neumann equation
Target entity description: The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
  • A. Schrödinger equation
    The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
  • B. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • C. Chapman–Kolmogorov equation
    The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
  • D. Tomonaga–Schwinger equation
    The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
  • E. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • 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_69c6888579d481909e05a8d6b81bf733 completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6e7d1652c8190973edceab55f04bc completed March 27, 2026, 8:25 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7ada12a848190b6e98e0b1a258c17 completed March 28, 2026, 10:29 a.m.
NEDg Description generation batch_69c7aeb1c59c8190b02fcb731003ad31 completed March 28, 2026, 10:34 a.m.
NED2 Entity disambiguation (via description) batch_69c7af2ad8a081909185cfd3a3d4e4d0 completed March 28, 2026, 10:36 a.m.
Created at: March 27, 2026, 2:46 p.m.