Born-Green equation

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Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle kT{\frac {\partial \ln {\rm {g}}(r_{12})}{\partial {\mathbf {r} }_{1}}}={\frac {-\partial U(r_{12})}{\partial {\mathbf {r} }_{1}}}-\rho \int \left[{\frac {\partial U(r_{13})}{\partial {\mathbf {r} }_{1}}}\right]{\rm {g}}(r_{13}){\rm {g}}(r_{23})~{\rm {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)