Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy

E461416

hierarchy of equations theoretical construct in statistical mechanics

The Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy is a set of coupled equations in statistical mechanics that describes the time evolution of reduced distribution functions for many-particle systems.

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Observed surface forms (3)

Surface form	Occurrences
BBGKY hierarchy	2
Boltzmann hierarchy	1
exact BBGKY hierarchy	1

Statements (43)

Predicate	Object
instanceOf	hierarchy of equations ⓘ theoretical construct in statistical mechanics ⓘ
alsoKnownAs	BBGKY hierarchy NERFINISHED ⓘ
appliesTo	classical many-body systems ⓘ many-particle systems ⓘ quantum many-body systems ⓘ
assumes	interacting particle systems ⓘ
basedOn	Liouville equation NERFINISHED ⓘ
concerns	phase-space distribution functions ⓘ reduced density matrices in quantum case ⓘ
describes	evolution of correlation functions in many-body systems ⓘ time evolution of reduced distribution functions ⓘ
domain	classical Hamiltonian systems ⓘ quantum statistical mechanics ⓘ
field	kinetic theory ⓘ statistical mechanics ⓘ
generalizes	BBGKY equations for higher-order correlations ⓘ
hasCharacteristic	infinite set of coupled integro-differential equations ⓘ requires closure approximation for practical use ⓘ
historicalPeriod	mid-20th century development in statistical mechanics ⓘ
mathematicalForm	coupled equations for reduced distribution functions f_s ⓘ
namedAfter	Herbert S. Green NERFINISHED ⓘ Jacques Yvon NERFINISHED ⓘ John G. Kirkwood NERFINISHED ⓘ Max Born NERFINISHED ⓘ Nikolay Bogoliubov NERFINISHED ⓘ
relatedTo	BBGKY hierarchy in quantum field theory formulations ⓘ Bogoliubov–Born–Green–Kirkwood formalism NERFINISHED ⓘ
relates	N-particle distribution functions of different orders ⓘ s-particle distribution function to (s+1)-particle distribution function ⓘ
requires	assumptions about molecular chaos for Boltzmann limit ⓘ
usedFor	derivation of kinetic equations ⓘ derivation of the Boltzmann equation ⓘ derivation of the Lenard–Balescu equation ⓘ derivation of the Vlasov equation ⓘ study of non-equilibrium statistical mechanics ⓘ study of relaxation to equilibrium ⓘ study of transport phenomena ⓘ
usedIn	condensed matter physics ⓘ kinetic theory of gases ⓘ nonequilibrium Green’s function methods NERFINISHED ⓘ plasma physics ⓘ theory of liquids ⓘ

Referenced by (5)

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

Nikolay Bogolyubov → notableWork → Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy ⓘ

Vlasov equation (for long-range interactions and negligible collisions) → relatedTo → Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy ⓘ

subject surface form: Vlasov equation

this entity surface form: BBGKY hierarchy

Kirkwood approximation in statistical mechanics → relatedTo → Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy ⓘ

subject surface form: Kirkwood approximation

this entity surface form: BBGKY hierarchy

Kirkwood approximation in statistical mechanics → contrastWith → Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy ⓘ

subject surface form: Kirkwood approximation

this entity surface form: exact BBGKY hierarchy

Boltzmann–Kac equation → relatedTo → Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy ⓘ

this entity surface form: Boltzmann hierarchy