Kac ring model
E92908
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kac model | 1 |
| Kac ring model canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T787792 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kac ring model Context triple: [Mark Kac, notableIdea, Kac ring model]
-
A.
Ising models
Ising models are mathematical models in statistical mechanics that describe systems of interacting binary variables (spins) on a lattice, widely used to study phase transitions, magnetism, and as a foundation for various probabilistic and machine learning models.
-
B.
Feynman checkerboard model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
-
C.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
D.
Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kac ring model Target entity description: The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
-
A.
Ising models
Ising models are mathematical models in statistical mechanics that describe systems of interacting binary variables (spins) on a lattice, widely used to study phase transitions, magnetism, and as a foundation for various probabilistic and machine learning models.
-
B.
Feynman checkerboard model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
-
C.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
D.
Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical model
ⓘ
model of irreversibility ⓘ statistical mechanics model ⓘ toy model ⓘ |
| analyzedUsing |
Markov chain methods
ⓘ
law of large numbers ⓘ probability theory ⓘ |
| assumes |
deterministic microscopic dynamics
ⓘ
discrete time steps ⓘ random initial distribution of scatterers ⓘ |
| demonstrates |
difference between microscopic reversibility and macroscopic irreversibility
ⓘ
role of probabilistic assumptions in thermodynamics ⓘ |
| describes | evolution of binary variables as particles move around a ring ⓘ |
| field |
mathematical physics
ⓘ
statistical mechanics ⓘ |
| hasComponent |
binary variables on sites
ⓘ
ring of sites ⓘ scatterers on bonds or sites ⓘ |
| hasDynamics |
binary variable flips when passing a scatterer
ⓘ
particles move one site per time step around the ring ⓘ |
| hasIdealization |
binary spin-like degrees of freedom
ⓘ
non-interacting particles ⓘ |
| hasLimitation |
does not include genuine interactions between particles
ⓘ
irreversibility is only apparent and statistical ⓘ |
| hasMacroscopicBehavior | irreversible ⓘ |
| hasMicroscopicDynamics | time-reversible ⓘ |
| hasProperty |
exactly solvable
ⓘ
finite number of degrees of freedom ⓘ non-Hamiltonian idealization ⓘ |
| illustrates |
Boltzmann’s idea of molecular chaos
ⓘ
how coarse-graining leads to apparent irreversibility ⓘ law of large numbers behavior in many-particle systems ⓘ |
| introducedBy | Mark Kac ⓘ |
| namedAfter | Mark Kac ⓘ |
| relatedTo |
Boltzmann equation
ⓘ
H-theorem ⓘ H-theorem ⓘ
surface form:
Loschmidt paradox
Poincaré recurrence theorem ⓘ
surface form:
Poincaré recurrence
kinetic theory ⓘ |
| shows |
entropy-like quantities can increase on average
ⓘ
recurrence at very long times for finite systems ⓘ |
| usedFor |
demonstrating time-reversal invariance at the microscopic level
ⓘ
illustrating macroscopic irreversibility ⓘ pedagogical explanation of the second law of thermodynamics ⓘ studying approach to equilibrium ⓘ |
| usedIn |
discussions of arrow of time
ⓘ
foundations of statistical mechanics ⓘ teaching thermodynamics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kac ring model Description of subject: The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kac model