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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 termsof the (logarithmic) Mahler measure of $P$. We extend the expansive case oftheir result to the noncommutative setting where $\mathbb{Z}^n$ gets replacedby suitable discrete amenable groups. Generalizing the Mahler measure,Fuglede-Kadison determinants from the theory of group von Neumann algebrasappear in the entropy formula.

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups