We extend the thermodynamic theory of gravitational clustering in an expanding universe to include the volume scale dependence of the ratio, b, of gravitational correlation energy to thermal energy. The predicted form of the gravitational quasi-equilibrium distribution function is unchanged by this scale dependence. This generalization of the theory contains no free parameters and clarifies many earlier results. It explains the improved agreement found previously between simulations, observations, and theory when b is allowed to depend on scale. Our new results are confirmed by comparisons with N-body simulations, which now agree to an accuracy of about 98%. The volume scale dependence of b has a number of consequences that add to our understanding of observational and theoretical aspects of gravitational clustering. We discuss its implications for the relation between the three-dimensional volume distribution functions and the two- dimensional projected distributions, for the interpretation of the scale- independent range of b, for the applicability of thermodynamic extensivity, for the resemblance between linear and nonlinear evolution of b, and for the role of the softening parameter in numerical simulations.