H-theorem

E57430

concept in thermodynamics result in kinetic theory theorem in statistical mechanics

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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All labels observed (4)

Label	Occurrences
H-theorem canonical	4
Boltzmann H-theorem	2
Loschmidt paradox	2
Boltzmann’s H-theorem	1

Statements (48)

Predicate	Object
instanceOf	concept in thermodynamics ⓘ result in kinetic theory ⓘ theorem in statistical mechanics ⓘ
aimsToExplain	why macroscopic processes are time-asymmetric ⓘ
appliesTo	dilute classical gas ⓘ non-equilibrium states near equilibrium ⓘ
associatedWith	Boltzmann equation for one-particle distribution function ⓘ
author	Ludwig Boltzmann ⓘ
basedOn	classical mechanics ⓘ time-reversible microscopic dynamics ⓘ
connects	microscopic dynamics and macroscopic thermodynamic behavior ⓘ
describes	approach to equilibrium in a dilute gas ⓘ
explains	entropy production in a dilute gas ⓘ macroscopic irreversibility from microscopic dynamics ⓘ
field	kinetic theory of gases ⓘ statistical mechanics ⓘ thermodynamics ⓘ
hasConsequence	Maxwell–Boltzmann statistics ⓘ surface form: equilibrium Maxwell–Boltzmann distribution
implies	monotonic decrease of H-function over time ⓘ monotonic increase of entropy-like quantity ⓘ
influenced	modern non-equilibrium statistical mechanics ⓘ philosophy of time’s arrow ⓘ
interpretation	entropy increase is overwhelmingly probable, not strictly necessary ⓘ
introducedIn	1870s ⓘ
involves	coarse-graining of microstates ⓘ collision term in Boltzmann equation ⓘ one-particle distribution function ⓘ
relatedConcept	Boltzmann’s entropy formula S = k log W ⓘ Boltzmann–Gibbs entropy in statistical mechanics ⓘ surface form: 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 ⓘ irreversible behavior emerges from probabilistic assumptions ⓘ
status	approximate result dependent on molecular chaos assumption ⓘ
subjectOf	H-theorem self-linksurface differs ⓘ surface form: Loschmidt paradox Zermelo recurrence objection ⓘ debates on foundations of statistical mechanics ⓘ
supports	statistical interpretation of the second law ⓘ
usesConcept	Boltzmann equation ⓘ surface form: Stosszahlansatz molecular chaos assumption ⓘ

Referenced by (9)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ludwig Boltzmann → notableIdea → H-theorem ⓘ

Boltzmann–Gibbs entropy in statistical mechanics → relatedTo → H-theorem ⓘ

subject surface form: Boltzmann–Gibbs entropy

Boltzmann equation → implies → H-theorem ⓘ

this entity surface form: Boltzmann H-theorem

Boltzmann equation → relatedTo → H-theorem ⓘ

H-theorem → subjectOf → H-theorem self-linksurface differs ⓘ

this entity surface form: Loschmidt paradox

Kac ring model → relatedTo → H-theorem ⓘ

this entity surface form: Loschmidt paradox

Boltzmann collision operator → relatedTo → H-theorem ⓘ

this entity surface form: Boltzmann H-theorem

Zermelo recurrence objection → critiques → H-theorem ⓘ

this entity surface form: Boltzmann’s H-theorem