  We derive the Einstein tensor from the Fisher information metric that is
defined by the probability distribution of a statistical mechanical system. We
find that the tensor naturally contains essential information of the
energy-momentum tensor of a classical scalar field, when the entropy data or
the spectrum data of the system are embedded into the classical field as the
field strength. Thus, we can regard the Einstein equation as the equation of
coarse-grained states for the original microscopic system behind the classical
field theory. We make some remarks on quantization of gravity and various
quantum-classical correspondences.
