  In the preceding paper, we derived a kind of kinematical holographic relation
(KHR) in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). It
essentially reflects the fundamental nature of the noncommutative geometry of
YSTA and its representation, that is, a definite kinematical reduction of
spatial degrees of freedom in comparison with the ordinary lattice space. On
the basis of the relation and its extension to various spatial dimensions, we
derive a new area-entropy relation in a simple $D_0$ brane gas system subject
to YSTA, following the idea of M-theory. Furthermore, we make clear its inner
relation with the Bekenstein-Hawking area-entropy relation in connection with
Schwarzschild black hole.
