Dynamical entropy and the third law of thermodynamics

We show that the third law of thermodynamics holds if the equilibrium states cluster appropriately in space and time uniformly for small temperatures. In this case, the entropy density and the dynamical entropy of the shift coincide. As an example in a one-dimensional lattice system with short-range interactions these cluster conditions are verified.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P6077P.