H-theorem
E57430
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.
Aliases (2)
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in thermodynamics
→
result in kinetic theory → theorem in statistical mechanics → |
| aimsToExplain |
why macroscopic processes are time-asymmetric
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|
| appliesTo |
dilute classical gas
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non-equilibrium states near equilibrium → |
| associatedWith |
Boltzmann equation for one-particle distribution function
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|
| author |
Ludwig Boltzmann
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|
| basedOn |
classical mechanics
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time-reversible microscopic dynamics → |
| connects |
microscopic dynamics and macroscopic thermodynamic behavior
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| describes |
approach to equilibrium in a dilute gas
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|
| explains |
entropy production in a dilute gas
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macroscopic irreversibility from microscopic dynamics → |
| field |
kinetic theory of gases
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statistical mechanics → thermodynamics → |
| hasConsequence |
equilibrium Maxwell–Boltzmann distribution
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| implies |
monotonic decrease of H-function over time
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monotonic increase of entropy-like quantity → |
| influenced |
modern non-equilibrium statistical mechanics
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philosophy of time’s arrow → |
| interpretation |
entropy increase is overwhelmingly probable, not strictly necessary
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| introducedIn |
1870s
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| involves |
coarse-graining of microstates
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collision term in Boltzmann equation → one-particle distribution function → |
| relatedConcept |
Boltzmann’s entropy formula S = k log W
→
Gibbs entropy → Poincaré recurrence theorem → coarse-grained entropy → ergodic hypothesis → |
| relatesTo |
Boltzmann entropy
→
Boltzmann equation → H-function → entropy increase → irreversibility → second law of thermodynamics → time-reversal invariance → |
| shows |
H-function is stationary at equilibrium
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irreversible behavior emerges from probabilistic assumptions → |
| status |
approximate result dependent on molecular chaos assumption
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| subjectOf |
Loschmidt paradox
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Zermelo recurrence objection → debates on foundations of statistical mechanics → |
| supports |
statistical interpretation of the second law
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|
| usesConcept |
Stosszahlansatz
→
molecular chaos assumption → |
Referenced by (7)
| Subject (surface form when different) | Predicate |
|---|---|
|
Boltzmann equation
→
Boltzmann–Gibbs entropy → Kac ring model → Kac ring model ("Loschmidt paradox") → |
relatedTo |
|
Boltzmann equation
("Boltzmann H-theorem")
→
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implies |
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Ludwig Boltzmann
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notableIdea |
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H-theorem
("Loschmidt paradox")
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subjectOf |