Systems in Stochastic Equilibrium
E695663
Systems in Stochastic Equilibrium is a seminal mathematical monograph by Peter Whittle that develops the theory of stochastic processes and their long-run equilibrium behavior in complex systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Systems in Stochastic Equilibrium canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7853055 — 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: Systems in Stochastic Equilibrium Context triple: [Peter Whittle, notableWork, Systems in Stochastic Equilibrium]
-
A.
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.
-
B.
dynamics of nonequilibrium systems
Dynamics of nonequilibrium systems is the field of physics that studies how physical systems evolve and organize over time when they are driven away from thermal or mechanical equilibrium.
-
C.
The Principles of Statistical Mechanics
The Principles of Statistical Mechanics is a classic 1938 textbook by Richard C. Tolman that systematically develops the foundations of statistical mechanics and its applications to thermodynamics and physical chemistry.
-
D.
Mathematical Foundations of Statistical Mechanics
Mathematical Foundations of Statistical Mechanics is a classic monograph by Aleksandr Khinchin that rigorously develops the probabilistic and measure-theoretic underpinnings of statistical mechanics.
-
E.
On Equilibrium
On Equilibrium is a philosophical work by John Ralston Saul that explores the importance of balancing key human qualities—such as reason, ethics, and common sense—to create a more humane and democratic society.
- 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: Systems in Stochastic Equilibrium Target entity description: Systems in Stochastic Equilibrium is a seminal mathematical monograph by Peter Whittle that develops the theory of stochastic processes and their long-run equilibrium behavior in complex systems.
-
A.
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.
-
B.
dynamics of nonequilibrium systems
Dynamics of nonequilibrium systems is the field of physics that studies how physical systems evolve and organize over time when they are driven away from thermal or mechanical equilibrium.
-
C.
The Principles of Statistical Mechanics
The Principles of Statistical Mechanics is a classic 1938 textbook by Richard C. Tolman that systematically develops the foundations of statistical mechanics and its applications to thermodynamics and physical chemistry.
-
D.
Mathematical Foundations of Statistical Mechanics
Mathematical Foundations of Statistical Mechanics is a classic monograph by Aleksandr Khinchin that rigorously develops the probabilistic and measure-theoretic underpinnings of statistical mechanics.
-
E.
On Equilibrium
On Equilibrium is a philosophical work by John Ralston Saul that explores the importance of balancing key human qualities—such as reason, ethics, and common sense—to create a more humane and democratic society.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| appliesTo |
communication systems models
ⓘ
complex systems with random dynamics ⓘ operations research models ⓘ queueing networks ⓘ |
| author | Peter Whittle ⓘ |
| contribution |
analyzes long‑run equilibrium behavior of stochastic processes
ⓘ
applies stochastic equilibrium concepts to applied probability models ⓘ develops a general framework for stochastic equilibrium in complex systems ⓘ |
| develops |
conditions for existence of stochastic equilibrium
ⓘ
conditions for uniqueness of stochastic equilibrium ⓘ methods for characterizing equilibrium distributions ⓘ techniques for analyzing stability of stochastic systems ⓘ |
| field |
applied mathematics
ⓘ
probability theory ⓘ stochastic modeling ⓘ stochastic processes ⓘ |
| genre |
mathematics literature
ⓘ
technical monograph ⓘ |
| hasImpactOn |
applied probability
ⓘ
queueing theory ⓘ stochastic control and optimization ⓘ theory of stochastic networks ⓘ |
| hasTheoreticalFocus |
equilibrium distributions
ⓘ
limiting behavior of random processes ⓘ rigorous analysis of stochastic systems ⓘ stability of stochastic systems ⓘ |
| influencedBy |
Markov process theory
ⓘ
ergodic theory ⓘ queueing theory ⓘ |
| intendedAudience |
advanced graduate students in probability and stochastic processes
ⓘ
operations researchers ⓘ probabilists ⓘ research mathematicians ⓘ |
| language | English ⓘ |
| mainSubject |
Markov processes
ⓘ
ergodic theory of stochastic processes ⓘ long‑run behavior of stochastic systems ⓘ queueing systems ⓘ stationary distributions ⓘ stochastic equilibrium ⓘ stochastic networks ⓘ |
| relatedTo |
Markov decision processes
ⓘ
renewal theory ⓘ stationary stochastic processes ⓘ |
| relatedWork |
Optimization Over Time
ⓘ
linked to:
Optimization over Time
Probability via Expectation ⓘ |
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: Systems in Stochastic Equilibrium Description of subject: Systems in Stochastic Equilibrium is a seminal mathematical monograph by Peter Whittle that develops the theory of stochastic processes and their long-run equilibrium behavior in complex systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.