  The possibility of generation of non-extensive statistics, in the sense of
Tsallis, due to space-time foam is discussed within the context of a particular
kind of foam in string/brane-theory, the D-particle foam model . The latter
involves point-like brane defects (D-particles), which provide the
topologically non-trivial foamy structures of space-time. A stochastic Langevin
equation for the velocity recoil of D-particles can be derived from the pinched
approximation for a sum over genera in the calculation of the partition
function of a bosonic string in the presence of heavy D-particles. The string
coupling in standard perturbation theory is related to the exponential of the
expectation of the dilaton. Inclusion of fluctuations of the dilaton itself and
uncertainties in the string background will then necessitate fluctuations in
$g_{s}$. The fluctuation in the string coupling in the sum over genera
typically leads to a generic structure of the Langevin equation where the
coefficient of the noise term, dependent on the string coupling $g_{s}$,
fluctuates. The positivity of $g_{s}$ leads naturally to a stochastic modelling
of its distribution with a $\chi$- distribution. This then rigorously implies a
Tsallis type non-extensive or, more generally, a superstatistics distribution
for the recoil velocity of D-particles. As a concrete and physically
interesting application, we provide a rigorous estimate of an $\omega$-like
effect, pertinent to CPT violating modifications of the Einstein-Podolsky-Rosen
correlators in entangled states of neutral Kaons. In the case of D-particle
foam fluctuations, which respect the Lorentz symmetry of the vacuum on average,
we find that the $\omega$-effect may be within the range of sensitivity of
future meson factories.

High Energy Physics - Theory;General Relativity and Quantum Cosmology