  We discuss two classes of semi-microscopic theoretical models of stochastic
space-time foam in quantum gravity and the associated effects on entangled
states of neutral mesons, signalling an intrinsic breakdown of CPT invariance.
One class of models deals with a specific model of foam, initially constructed
in the context of non-critical (Liouville) string theory, but viewed here in
the more general context of effective quantum-gravity models. The relevant
Hamiltonian perturbation, describing the interaction of the meson with the foam
medium, consists of off-diagonal stochastic metric fluctuations, connecting
distinct mass eigenstates (or the appropriate generalisation thereof in the
case of K-mesons), and it is proportional to the relevant momentum transfer
(along the direction of motion of the meson pair). There are two kinds of
CPT-violating effects in this case, which can be experimentally disentangled:
one (termed ``omega-effect'') is associated with the failure of the
indistinguishability between the neutral meson and its antiparticle, and
affects certain symmetry properties of the initial state of the two-meson
system; the second effect is generated by the time evolution of the system in
the medium of the space-time foam, and can result in time-dependent
contributions of the $omega-effect type in the time profile of the two meson
state. Estimates of both effects are given, which show that, at least in
certain models, such effects are not far from the sensitivity of experimental
facilities available currently or in the near future. The other class of
quantum gravity models involves a medium of gravitational fluctuations which
behaves like a ``thermal bath''. In this model both of the above-mentioned
intrinsic CPT violation effects are not valid.
