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## Boltzmann equation
## Additional recommended knowledgeThe The Boltzmann equation is an equation for the time - is proportional to the number of particles in the phase-space volume
*d***x***d***p**at time*t*.
Consider those particles described by - ,
that is, the particle density in Dividing the equation by
## Stosszahl AnsatzThe above Boltzmann equation is of little practical use as it leaves the collision term unspecified. A key insight applied by 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 'Stosszahl Ansatz', 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: ## Extensions and applicationsIt is also possible to write down relativistic Boltzmann equations for systems in which a number of particle species can collide and produce different species. This is how the formation of the light elements in big bang nucleosynthesis is calculated. The Boltzmann equation is also often used in dynamics, especially galactic dynamics. A galaxy, under certain assumptions, may be approximated as a continuous fluid; its mass distribution is then represented by In Hamiltonian mechanics, the Boltzmann equation is often written more generally as - ,
where and the generalization to (general) relativity is where The name Boltzmann equation is also given to this equation: |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Boltzmann_equation". A list of authors is available in Wikipedia. |