Gibbs paradox
E517576
The Gibbs paradox is a concept in thermodynamics and statistical mechanics highlighting an apparent contradiction in the entropy change when mixing identical versus distinct gases, which helped clarify the role of particle indistinguishability.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gibbs paradox canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5390039 — 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: Gibbs paradox Context triple: [Josiah Willard Gibbs, knownFor, Gibbs paradox]
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A.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
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B.
Carathéodory’s formulation of the second law of thermodynamics
Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.
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C.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
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D.
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.
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E.
Clausius theorem
The Clausius theorem is a fundamental result in thermodynamics that formalizes the second law by relating the cyclic integral of heat transfer over temperature to entropy, showing that this quantity is always less than or equal to zero for any cyclic process.
- 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: Gibbs paradox Target entity description: The Gibbs paradox is a concept in thermodynamics and statistical mechanics highlighting an apparent contradiction in the entropy change when mixing identical versus distinct gases, which helped clarify the role of particle indistinguishability.
-
A.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
-
B.
Carathéodory’s formulation of the second law of thermodynamics
Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.
-
C.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
-
D.
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.
-
E.
Clausius theorem
The Clausius theorem is a fundamental result in thermodynamics that formalizes the second law by relating the cyclic integral of heat transfer over temperature to entropy, showing that this quantity is always less than or equal to zero for any cyclic process.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in statistical mechanics
ⓘ
entropy paradox ⓘ thermodynamics paradox ⓘ |
| appearsIn | discussions of thermodynamic extensivity ⓘ |
| category |
paradoxes in physics
ⓘ
thermodynamic entropy ⓘ |
| concerns |
mixing of distinct gases
ⓘ
mixing of identical gases ⓘ |
| concernsProperty | extensivity of entropy ⓘ |
| describes | apparent contradiction in entropy change ⓘ |
| discussedIn |
foundations of thermodynamics literature
ⓘ
textbooks on statistical mechanics ⓘ |
| field |
statistical mechanics
ⓘ
thermodynamics ⓘ |
| hasConsequence |
corrects overcounting of microstates
ⓘ
ensures continuity of entropy as gases become identical ⓘ |
| highlights |
difference between classical and quantum descriptions of particles
ⓘ
need for indistinguishability postulate in statistical mechanics ⓘ role of labeling in counting microstates ⓘ |
| historicalImpact |
clarified foundations of statistical mechanics
ⓘ
motivated adoption of indistinguishability in quantum theory ⓘ |
| implies | entropy of mixing for identical gases should be zero ⓘ |
| involvesConcept |
classical statistics
ⓘ
entropy of mixing ⓘ ideal gas ⓘ particle indistinguishability ⓘ quantum statistics ⓘ |
| involvesProcess | mixing of gases ⓘ |
| involvesQuantity | entropy ⓘ |
| namedAfter | Josiah Willard Gibbs NERFINISHED ⓘ |
| occursWhen |
classical particles are treated as distinguishable
ⓘ
two gas samples have same macroscopic properties ⓘ |
| relatedTo |
Boltzmann entropy formula
NERFINISHED
ⓘ
S = k_B ln W ⓘ Sackur–Tetrode equation NERFINISHED ⓘ Shannon entropy NERFINISHED ⓘ ideal gas entropy ⓘ information-theoretic entropy ⓘ mixing entropy ⓘ |
| resolutionInvolves |
division by N! in counting microstates
ⓘ
indistinguishability of identical particles ⓘ quantum mechanical treatment of identical particles ⓘ use of correct combinatorial factors in statistical mechanics ⓘ |
| resolvedBy |
treating identical particles as indistinguishable
ⓘ
using quantum statistics for identical particles ⓘ |
| states | entropy of mixing appears nonzero for identical gases in classical treatment ⓘ |
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: Gibbs paradox Description of subject: The Gibbs paradox is a concept in thermodynamics and statistical mechanics highlighting an apparent contradiction in the entropy change when mixing identical versus distinct gases, which helped clarify the role of particle indistinguishability.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.