HIERARCHY OF EQUATIONS FOR REDUCED DENSITY-MATRICES IN THE CASE OF THERMODYNAMIC-EQUILIBRIUM

A hierarchy of equations for s-particle density matrices at thermodyna mic equilibrium is obtained, with the equation for the nonequilibrium density matrix as the starting point. When deducing the hierarchy the hypothesis of maximum statistical independence for the density matrice s is used. The hierarchy obtained is an analogue of the classical equi librium BBGKY hierarchy and goes over into it when h --> 0. It is show n that thermodynamic quantities can be expressed in terms of functions that enter only into the first hierarchy equations. The hierarchy is analysed in detail in the case of a uniform fluid. As an example in wh ich the equations can be solved easily enough, a hard-sphere system wh erein triplet correlations are neglected is considered. Different appr oximations that can be used when solving the equations derived are dis cussed. Comparisons are made with the results of other theoretical tre atments.