In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain
Z
n
\mathbb {Z}^n
-dynamical systems attached to Laurent polynomials
P
P
, in terms of the (logarithmic) Mahler measure of
P
P
. We extend the expansive case of their result to the noncommutative setting where
Z
n
\mathbb {Z}^n
gets replaced by suitable discrete amenable groups. Generalizing the Mahler measure, Fuglede–Kadison determinants from the theory of group von Neumann algebras appear in the entropy formula.