Space-time dynamical entropy of quantum systems

The definition of the dynamical entropy for single auto-morphisms of nuclear C*-algebras is extended to groups of several commuting automorphisms. This entropy of a Zν-action is shown to be nonzero only if all the corresponding Zμ-'subactions' (0<μ<ν) have infinite entropy. As a simple consequence, the space-time entropy of quantum lattice spin systems, and of one-dimensional continuous systems with 'physically reasonable' quasifree states, vanishes. 22 refs. (Author)