Boltzmann equation

E46431
equation in statistical mechanics integro-differential equation kinetic equation transport equation

The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.

Jump to: Surface forms Statements Referenced by

Observed surface forms (3)

Surface form Occurrences
Stosszahlansatz 1
linearized Boltzmann equation 1
relativistic Boltzmann equation 1

Statements (49)

Predicate Object
instanceOf equation in statistical mechanics ⓘ
integro-differential equation ⓘ
kinetic equation ⓘ
transport equation ⓘ
appliesTo classical particles ⓘ
dilute gases ⓘ
assumes binary collisions ⓘ
molecular chaos ⓘ
short-range interactions ⓘ
describes effect of collisions on particle distributions ⓘ
evolution in phase space ⓘ
free streaming of particles ⓘ
non-equilibrium dynamics of gases ⓘ
statistical behavior of a dilute gas ⓘ
time evolution of particle distribution function ⓘ
domain phase space ⓘ
field gas dynamics ⓘ
kinetic theory ⓘ
mathematical physics ⓘ
statistical mechanics ⓘ
governs approach to thermodynamic equilibrium in gases ⓘ
hasDependentVariable single-particle distribution function ⓘ
hasIndependentVariable momentum ⓘ
position ⓘ
time ⓘ
velocity ⓘ
hasLimit Euler equations ⓘ
surface form: Euler equations (hydrodynamic limit)

Navier–Stokes equations ⓘ
surface form: Navier–Stokes equations (hydrodynamic limit with viscosity)

Vlasov equation (for long-range interactions and negligible collisions) ⓘ
hasVariant Boltzmann–BGK equation ⓘ
Boltzmann equation self-linksurface differs ⓘ
surface form: linearized Boltzmann equation

quantum Boltzmann equation ⓘ
Boltzmann equation self-linksurface differs ⓘ
surface form: relativistic Boltzmann equation
historicalPeriod late 19th century ⓘ
implies H-theorem ⓘ
surface form: Boltzmann H-theorem
includesOperator Boltzmann collision operator ⓘ
includesTerm collision term ⓘ
streaming term ⓘ
mathematicalType integro-differential equation in 7 variables ⓘ
nonlinear equation ⓘ
namedAfter Ludwig Boltzmann ⓘ
relatedTo Boltzmann–Gibbs entropy in statistical mechanics ⓘ
surface form: Boltzmann entropy

H-theorem ⓘ
Maxwell–Boltzmann statistics ⓘ
surface form: Maxwell–Boltzmann distribution
usedFor derivation of Navier–Stokes equations ⓘ
derivation of hydrodynamic equations ⓘ
non-equilibrium statistical mechanics ⓘ
rarefied gas dynamics ⓘ
transport coefficients calculation ⓘ

Referenced by (10)

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

Ludwig Boltzmann → hasEquationNamedAfter → Boltzmann equation ⓘ
Boltzmann equation → hasVariant → Boltzmann equation self-linksurface differs ⓘ
this entity surface form: relativistic Boltzmann equation
Boltzmann equation → hasVariant → Boltzmann equation self-linksurface differs ⓘ
this entity surface form: linearized Boltzmann equation
Ludwig Boltzmann → knownFor → Boltzmann equation ⓘ
Radiative Transfer → relatedConcept → Boltzmann equation ⓘ
Kac ring model → relatedTo → Boltzmann equation ⓘ
Kac walk → relatedTo → Boltzmann equation ⓘ
Smoluchowski coagulation equation → relatedTo → Boltzmann equation ⓘ
H-theorem → relatesTo → Boltzmann equation ⓘ
H-theorem → usesConcept → Boltzmann equation ⓘ
this entity surface form: Stosszahlansatz