We construct a new class of semigroups of completely positive maps on which can be decomposed into an infinite tensor product of such semigroups. Under suitable hypotheses, the minimal dilations
of these semigroups to E
0-semigroups are pure, and have no normal invariant states. Concrete examples are discussed in some detail.
A new definition of critical dilation is propose for use in ASTM Test Method for Critical Dilation of Concrete Specimens Subjected to Freezing (C 671). Using this definition, only a single cycle of freezing is needed to determine whether or not a specimen is frost resistant.