Born-Green equation

$kT\frac{\partial \ln \mathrm{g}(r_{12})}{\partial {\mathbf{r}}_1}=\frac{-\partial U(r_{12})}{\partial {\mathbf{r}}_1}-\rho \int [\frac{\partial U(r_{13})}{\partial {\mathbf{r}}_1}]\mathrm{g}(r_{13})\mathrm{g}(r_{23})\mathrm{d}{\mathbf{r}}_3$

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)