If energy is applied, the result is not "spontaneous." Furthermore, both the applied energy and its result are, by virtue of design, quantifiable mathematically.
In thermodynamics, spontaneous means that any energy available in an object for diffusing will spread out if given a chance.
The applied energy and its result are indeed quantifiable mathematically, but it has nothing to do with design. Its a part of the natural interactions between atoms. Being quantifiable mathematically does not imply design.