A previous brief summary of some basic relations in non-Hamiltonian statistical mechanics (Ramshaw J. D., Phys. Lett. A, 116 (1986) 110) is generalized to allow for an arbitrary time-dependent metric in phase space, thereby permitting a comparison with the formulation of Tuckerman et al. (TEA) (Europhys. Lett., 45 (1999) 149). It is shown that a) the generalized Liouville equation (GLE) in the earlier work is rigorously valid in general, and moreover is completely equivalent to the GLE of TEA; and b) the time-dependent metric factor √g in the volume form used by TEA is itself a solution of the GLE, and consequently becomes singular and unacceptable for systems with attractors in steady state. At the time of writing, John Ramshaw was affiliated with Lawrence Livermore National Laboratory.