Ehrenfest model
E735840
The Ehrenfest model is a classic probabilistic model in statistical mechanics that illustrates the approach to equilibrium and fluctuations in a gas by tracking particles randomly moving between two containers.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ehrenfest model canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T8490718 — 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: Ehrenfest model Context triple: [Paul Ehrenfest, notableWork, Ehrenfest model]
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A.
Kac ring model
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.
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B.
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.
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C.
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.
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D.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
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E.
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.
- 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: Ehrenfest model Target entity description: The Ehrenfest model is a classic probabilistic model in statistical mechanics that illustrates the approach to equilibrium and fluctuations in a gas by tracking particles randomly moving between two containers.
-
A.
Kac ring model
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.
-
B.
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.
-
C.
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.
-
D.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
E.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
Markov chain
ⓘ
model in statistical mechanics ⓘ probabilistic model ⓘ urn model ⓘ |
| alsoKnownAs | Ehrenfest urn model ⓘ |
| demonstrates |
law of large numbers behavior for large N
ⓘ
typicality of equilibrium macrostate ⓘ |
| describes | random motion of particles between two containers ⓘ |
| equilibriumDistribution | binomial distribution ⓘ |
| equilibriumProperty | satisfies detailed balance ⓘ |
| field |
probability theory
ⓘ
statistical mechanics ⓘ stochastic processes ⓘ |
| hasComponent |
N indistinguishable particles
ⓘ
two urns ⓘ |
| hasParameter | number of particles N ⓘ |
| hasProperty |
aperiodic
ⓘ
ergodic ⓘ irreducible ⓘ time-homogeneous ⓘ |
| illustratesConcept |
Boltzmann’s H-theorem
ⓘ
linked to:
H-theorem
fluctuations around equilibrium ⓘ macroscopic irreversibility from microscopic reversibility ⓘ recurrence ⓘ |
| mathematicalTool |
Markov chain theory
ⓘ
linked to:
Markov processes
binomial coefficients ⓘ stochastic convergence ⓘ |
| models | approach to thermodynamic equilibrium ⓘ |
| namedAfter |
Paul Ehrenfest
ⓘ
Tatiana Ehrenfest ⓘ
linked to:
Tatiana Ehrenfest-Afanassjewa
|
| originalContext | kinetic theory of gases ⓘ |
| purpose |
illustrate approach to equilibrium
ⓘ
illustrate fluctuations in a gas ⓘ |
| relatedTo |
Boltzmann equation
ⓘ
birth–death process ⓘ random walk on the hypercube ⓘ |
| stateSpace | number of particles in one urn ⓘ |
| stateSpaceType | finite ⓘ |
| timeReversalProperty | microscopically reversible ⓘ |
| transitionGraph | birth–death chain ⓘ |
| transitionRule | at each step one particle is chosen at random and moved to the other urn ⓘ |
| transitionType | discrete-time ⓘ |
| typicalAssumption |
all particles are equally likely to be chosen
ⓘ
particles are non-interacting ⓘ |
| usedIn |
studies of mixing times
ⓘ
studies of relaxation to equilibrium ⓘ teaching Markov chains ⓘ teaching statistical mechanics ⓘ |
| yearProposed | 1907 ⓘ |
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: Ehrenfest model Description of subject: The Ehrenfest model is a classic probabilistic model in statistical mechanics that illustrates the approach to equilibrium and fluctuations in a gas by tracking particles randomly moving between two containers.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Ehrenfest