npub1c9m22hkc5h6zgrwkz48crhcpw6vch2rf6j97746ugl3neys86jeqyz9xjd (npub1c9m…9xjd) (2)
If that "product" was a "sum", this would match up better with the statistical "variance" approach. So a volume (determinant) vs. trace distinction.
I had that before with estimating the temperature (<E^2>) vs. the phase space volume of a multidimensional distribution recently. Temperature was the trace of the covariance matrix, phase space volume was the determinant.