Abstract
The definition of the dynamical entropy for single automorphisms of nuclear C*-algebras is extended to groups of several commuting automorphisms. This entropy of a Zv-action is shown to be nonzero only if all the corresponding Zμ-‘subactions’ (0<μ<v) have infinite entropy. As a simple consequence, the spacetime entropy of quantum lattice spin systems, and of one-dimensional continuous systems with ‘physically reasonable’ quasifree states, vanishes.
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