Abstract. In 1989, B.Kitchens and K. Schmidt introduced an algebraic approach to the study of abelian actions of automorphisms of compact groups. One year later, D.Lind, T.Ward and K. Schmidt were able to compute entropy in this new language. In the case of principal actions the entropy is given by a logarithmic Mahler measure. Recently, C. Deninger and K. Schmidt could compute the entropy of certain non-abelian actions in terms of the Fuglede- Kadison determinant of the associated von Neumann-algebras. These are however notoriously hard to estimate. I will discuss a new approach to get lower estimates of the entropy of actions of the discrete Heisenberg group using potential theory. Joint work with D. Lind.