Born-Green equation

The Born-Green equation is given by:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi (r_{nm})} is the intermolecular pair potential, T is the temperature, and $k_{B}$ is the Boltzmann constant.

References

1. 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)