From these considerations we see that, if we wish to calculate the way in which a thermodynamic process takes place in time, such a formulation of initial and boundary conditions as is perfectly sufficient for a unique determination of the process in thermodynamics, does not suffice for the mechanical theory of heat or for the electrodynamical theory of heat radiation.
On the contrary, from the standpoint of pure mechanics or electrodynamics the solutions of the problem are infinite in number.
Hence, unless we wish to renounce entirely the possibility of representing the thermodynamic processes mechanically or electrodynamically, there remains only one way out of the difficulty, namely, to supplement the initial and boundary conditions by special hypotheses of such a nature that the mechanical or electrodynamical equations will lead to an unambiguous result in agreement with experience.
As to how such an hypothesis is to be formulated, no hint can naturally be obtained from the principles of mechanics or electrodynamics, for they leave the question entirely open.
Just on that account any mechanical or electrodynamical hypothesis containing some further specialization of the given initial and boundary conditions, which cannot be tested by direct measurement, is admissible a priori. What hypothesis is to be preferred can be decided only by testing the results to which it leads in the light of the thermodynamic principles based on experience.