  In the context of an idealized model describing an atom coupled to black-body
radiation at a sufficiently high positive temperature, we show that the atom
will end up being ionized in the limit of large times. Mathematically, this is
translated into the statement that the coupled system does not have any
time-translation invariant state of positive (asymptotic) temperature, and that
the expectation value of an arbitrary finite-dimensional projection in an
arbitrary initial state of positive (asymptotic) temperature tends to zero, as
time tends to infinity.
  These results are formulated within the general framework of $W^*$-dynamical
systems, and the proofs are based on Mourre's theory of positive commutators
and a new virial theorem. Results on the so-called standard form of a von
Neumann algebra play an important role in our analysis.
