Fokker–Planck equation
E8633
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.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Fokker–Planck equation canonical | 13 |
| Kolmogorov forward equation | 5 |
| Smoluchowski diffusion equation | 2 |
| Ornstein–Uhlenbeck process | 1 |
| forward Kolmogorov equation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T79819 — 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: Fokker–Planck equation Context triple: [Brownian motion, relatedConcept, Fokker–Planck equation]
-
A.
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.
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B.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
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C.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
-
D.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
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E.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
- 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: Fokker–Planck equation Target entity description: 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.
-
A.
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.
-
B.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
-
C.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
-
D.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
-
E.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
evolution equation
ⓘ
partial differential equation ⓘ stochastic process equation ⓘ |
| alsoKnownAs |
Fokker–Planck equation
ⓘ
surface form:
forward Kolmogorov equation
|
| appliesTo |
Markovian dynamics
ⓘ
systems with Gaussian noise ⓘ |
| assumes | Markov property ⓘ |
| canBeDerivedFrom | Langevin dynamics ⓘ |
| canBeWrittenIn | conservation form ⓘ |
| describes |
Brownian motion
ⓘ
time evolution of probability density functions ⓘ time evolution of stochastic processes ⓘ |
| expresses | conservation of probability ⓘ |
| field |
applied mathematics
ⓘ
mathematical physics ⓘ probability theory ⓘ |
| generalizes | classical diffusion equation ⓘ |
| governs | probability density function ⓘ |
| hasSolutionType | probability density function over state space ⓘ |
| hasTerm |
diffusion term
ⓘ
drift term ⓘ |
| models |
Markov processes
ⓘ
continuous-time stochastic processes ⓘ diffusion with drift ⓘ |
| namedAfter |
Adriaan Fokker
ⓘ
Max Planck ⓘ |
| relatedTo |
Kolmogorov backward equation
ⓘ
Langevin dynamics ⓘ
surface form:
Langevin equation
Ornstein–Uhlenbeck process ⓘ diffusion equation ⓘ master equation ⓘ |
| timeDependent | yes ⓘ |
| type | second-order partial differential equation ⓘ |
| usedFor |
escape rate calculations
ⓘ
first-passage time problems ⓘ noise-induced transitions ⓘ non-equilibrium statistical mechanics ⓘ transport phenomena ⓘ |
| usedIn |
chemical physics
ⓘ
diffusion theory ⓘ financial mathematics ⓘ neuroscience ⓘ plasma physics ⓘ population dynamics ⓘ quantum optics ⓘ statistical physics ⓘ stochastic processes ⓘ |
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: Fokker–Planck equation Description of subject: 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.
Referenced by (22)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kolmogorov forward equation
this entity surface form:
Ornstein–Uhlenbeck process
this entity surface form:
forward Kolmogorov equation
this entity surface form:
Smoluchowski diffusion equation
subject surface form:
Markov process
this entity surface form:
Kolmogorov forward equation
this entity surface form:
Kolmogorov forward equation
this entity surface form:
Smoluchowski diffusion equation
this entity surface form:
Kolmogorov forward equation
this entity surface form:
Kolmogorov forward equation