  Quantitative estimates are derived, on the whole space, for the relative
entropy between the joint law of random interacting particles and the
tensorized law at the limiting systeme. The developed method combines the
relative entropy method under the moderated interaction scaling introduced by
Oeschl\"ager, and the propagation of chaos in probability. The result includes
the case that the interaction force does not need to be a potential field.
Furthermore, if the interaction force is a potential field, with a
convolutional structure, then the developed estimate also provides the
modulated energy estimates. Moreover, we demonstrate propagation of chaos for
large stochastic systems of interacting particles and discuss possible
applications to various interacting particle systems, including the Coulomb
interaction case.
