Average quantal behavior and thermodynamic isolation

We study the thermodynamic concept of isolation. The causal motion of a system that models a thermodynamic universe but nevertheless couples to a surround is reconciled with an increase of entropy-in the manner of the second law of thermodynamics-for the system. The system's ket space isn-dimensional, the surround's isK -dimensional, and the initial state is taken purepure: the tensor product of a puren-state with a pureK-state. Near-maximal entropy is found for the reducedn-state in deep time, first for most random Hamiltonians, then also under restriction to weakn-K coupling-but then with a shortfall of about 1 bit.