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==The collision term (Stosszahlansatz) and molecular chaos==

==The collision term (Stosszahlansatz) and molecular chaos==

===Two-body collision term ===

===Two-body collision term ===

A key insight applied by [[Ludwig Boltzmann|Boltzmann]] was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the "''Stosszahlansatz'' " and is also known as the "[[molecular chaos]] assumption". Under this assumption the collision term can be written as a momentum-space integral over the product of one-particle distribution functions:<ref name="Encyclopaediaof" />

 

 

A key insight applied by [[Ludwig Boltzmann|Boltzmann]] was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the "{{lang|de|Stosszahlansatz}}" and is also known as the "[[molecular chaos]] assumption". Under this assumption the collision term can be written as a momentum-space integral over the product of one-particle distribution functions:<ref name="Encyclopaediaof" />

 

 

:<math>

:<math>

is the magnitude of the relative momenta (see [[relative velocity]] for more on this concept), and ''I''(''g'', Ω) is the [[differential cross section]] of the collision, in which the relative momenta of the colliding particles turns through an angle θ into the element of the [[solid angle]] ''d''Ω, due to the collision.

is the magnitude of the relative momenta (see [[relative velocity]] for more on this concept), and ''I''(''g'', Ω) is the [[differential cross section]] of the collision, in which the relative momenta of the colliding particles turns through an angle θ into the element of the [[solid angle]] ''d''Ω, due to the collision.

===Simplifications to the collision term===

===Simplifications to the collision term===

| last1= Arkeryd  

| last1= Arkeryd  

| last1= Arkeryd

| last1= Arkeryd  

 

 

 

 

 

[[分类:偏微分方程]]

[[分类:偏微分方程]]

[[分类:统计力学]]

[[分类:统计力学]]