  In 1990, Lind, Schmidt and Ward gave a formula for the entropy of certain
$\mathbb{Z}^n$-dynamical systems attached to Laurent polynomials $P$, in terms
of the (logarithmic) Mahler measure of $P$. We extend the expansive case of
their result to the noncommutative setting where $\mathbb{Z}^n$ 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.
