TY - JOUR

T1 - Long-range correlations in a closed system with applications to nonuniform fluids

AU - Lebowitz, J. L.

AU - Percus, J. K.

PY - 1961

Y1 - 1961

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRev.122.1675

DO - 10.1103/PhysRev.122.1675

M3 - Article

AN - SCOPUS:4243692101

VL - 122

SP - 1675

EP - 1691

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 6

ER -