Onsager–Machlup function
E163913
concept in nonequilibrium statistical mechanics
concept in stochastic process theory
mathematical functional
tool in large deviation theory
The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Onsager–Machlup function canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1432641 — 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: Onsager–Machlup function Context triple: [Lars Onsager, knownFor, Onsager–Machlup function]
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A.
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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B.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
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C.
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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D.
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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E.
Boltzmann–Gibbs entropy in statistical mechanics
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
- 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: Onsager–Machlup function Target entity description: The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
-
A.
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.
-
B.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
C.
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.
-
D.
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.
-
E.
Boltzmann–Gibbs entropy in statistical mechanics
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
concept in nonequilibrium statistical mechanics
ⓘ
concept in stochastic process theory ⓘ mathematical functional ⓘ tool in large deviation theory ⓘ |
| appliesTo |
Langevin dynamics
ⓘ
continuous-time stochastic processes ⓘ diffusion processes ⓘ |
| assumes | Markovian dynamics in standard formulations ⓘ |
| characterizes | most probable paths of fluctuating systems ⓘ |
| dependsOn |
diffusion coefficient
ⓘ
drift term of the stochastic differential equation ⓘ time-discretization scheme ⓘ |
| describes | weight of a path in configuration space ⓘ |
| field |
large deviation theory
ⓘ
nonequilibrium statistical mechanics ⓘ statistical physics ⓘ stochastic processes ⓘ |
| generalizedTo |
manifold-valued stochastic processes
ⓘ
multiplicative noise ⓘ non-Gaussian noise ⓘ |
| historicalContext | introduced in mid-20th century ⓘ |
| mathematicalForm | time integral of a Lagrangian-like density along a path ⓘ |
| namedAfter |
Lars Onsager
ⓘ
Stefan Machlup ⓘ |
| relatedTo |
Fokker–Planck equation
ⓘ
Freidlin–Wentzell theory ⓘ Langevin dynamics ⓘ
surface form:
Langevin equation
Onsager reciprocal relations ⓘ large deviation principle ⓘ path integral formulation of stochastic processes ⓘ |
| role |
effective action for stochastic trajectories
ⓘ
rate functional in certain large deviation problems ⓘ |
| usedBy |
applied mathematicians
ⓘ
engineers studying stochastic dynamics ⓘ statistical physicists ⓘ theoretical chemists ⓘ |
| usedFor |
action functional in stochastic systems
ⓘ
most probable fluctuation paths ⓘ path probability densities ⓘ variational characterization of stochastic trajectories ⓘ |
| usedIn |
nonequilibrium thermodynamics of small systems
ⓘ
rare event sampling methods ⓘ stochastic control and optimization ⓘ theory of fluctuations around steady states ⓘ transition path theory ⓘ |
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: Onsager–Machlup function Description of subject: The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.