Born-Green equation

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The Born-Green equation is given by:

$k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}= \frac{-\partial \Phi(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial \Phi(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3$

where $Φ(r n m)$ is the intermolecular pair potential, T is the temperature, and $k B$ is the Boltzmann constant.

[edit] References

M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 188 pp. 10-18 (1946)

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Category: Statistical mechanics

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