But what mechanical or electrodynamical quantity represents the entropy of a state? It is evident that this quantity depends in some way on the "probability" of the state. For since an elemental chaos and the absence of a record of any individual element forms an essential feature of entropy, the tendency to neutralize any existing temperature differences, which is connected with an increase of entropy, can mean nothing for the mechanical or electrodynamical observer but that uniform
distribution of elements in a chaotic state is more probable than any other distribution.
Now since the concept of entropy as well as the second principle of thermodynamics are of universal application, and since on the other hand the laws of probability have no less universal validity, it is to be expected that the connection between entropy and probability should be very close. Hence we make the following proposition the foundation of our further discussion:
The entropy of a physical system in a definite state depends solely on the probability of this state. The fertility of this law will be seen later in several cases. We shall not, however, attempt to give a strict general proof of it at this point. In fact, such an attempt evidently would have no meaning at this point. For, so long as the "probability" of a state is not numerically defined, the correctness of the proposition cannot be quantitatively tested. One might, in fact, suspect at first sight that on this account the proposition has no definite physical meaning. It may, however, be shown by a simple deduction that it is possible by means of this fundamental proposition to determine quite generally the way in which entropy depends on probability, without any further discussion of the probability of a state.