### Abstract

We investigate the corrections to the representation of the joint distribution of q+l particles, nq+l, by the product nqnl for large separation between the sets of q and l particles. For a system in which there exists a "finite correlation length," we find explicitly the 1N correction term to the simple product, where N is the number of particles in our system. When q+l is equal to two, this expression reduces to that familiar from the Ornstein-Zernike relations for scattering of light from a fluid. In a uniform gas, our derivation also yields the explicit 1N dependence of equilibrium distributions. Our result on the asymptotic form is then used to determine the low-order distribution functions for an equilibrium system of varying density, as well as for a nonequilibrium system represented by a local-equilibrium ensemble. These distribution functions are shown to be governed by the temperature and density in the vicinity of the molecules considered. We find as expected that the two-body distribution function coincides, to within quadratic terms in the gradients, with its equilibrium value for a uniform system at the temperature and density of the midpoint. For the higher-order distributions, correction terms linear in the gradients are found.

Original language | English (US) |
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Pages (from-to) | 1675-1691 |

Number of pages | 17 |

Journal | Physical Review |

Volume | 122 |

Issue number | 6 |

DOIs | |

State | Published - 1961 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physical Review*,

*122*(6), 1675-1691. https://doi.org/10.1103/PhysRev.122.1675