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.
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
NERFINISHED
ⓘ
fluctuations around equilibrium ⓘ macroscopic irreversibility from microscopic reversibility ⓘ recurrence ⓘ |
| mathematicalTool |
Markov chain theory
NERFINISHED
ⓘ
binomial coefficients ⓘ stochastic convergence ⓘ |
| models | approach to thermodynamic equilibrium ⓘ |
| namedAfter |
Paul Ehrenfest
NERFINISHED
ⓘ
Tatiana Ehrenfest NERFINISHED ⓘ |
| originalContext | kinetic theory of gases ⓘ |
| purpose |
illustrate approach to equilibrium
ⓘ
illustrate fluctuations in a gas ⓘ |
| relatedTo |
Boltzmann equation
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.