Mahler measure, Fuglede-Kadison determinants and entropy of algebraic systems

Lind-Schmidt-Ward proved the logarithmic Mahler measure of an integral polynomial equals the entropy of a corresponding dynamical system (building on pioneering work of Yuzvniskii). After a breakthrough due to Deninger, this equality has been generalized greatly over recent years by several authors to an equality between the Fuglede-Kadison determinant of an element of the integral group ring of a group G and the sofic entropy of a corresponding action of G by automorphisms on a compact abelian group.

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