  We extend the notion of intrinsic entropy for endomorphisms of Abelian groups
to endomorphisms of modules over an Archimedean non-discrete valuation domain
$R$, using the natural non-discrete length function introduced by Northcott and
Reufel for such a category of modules. We prove that this notion of entropy is
a length function for the category of $R[X]$-modules, it satisfies (a suitably
adapted version of) the Intrinsic Algebraic Yuzvinski Formula and that it is
essentially the unique invariant for $Mod(R[X])$ with these properties.
