The requirement that the sum on the two cubes shall be 2, however, involves but one complexion. Under the circumstances therefore the probability of throwing the sum 4 is three times as great as throwing the sum 2.
In closing this part of our presentation, we may make what is now an almost obvious remark. The long-lasting difficulty in giving a physical meaning to entropy and the Second Law is due to the fact of its intimate dependence on considerations of probability. It is only quite recently that such considerations have attained the dignity of a great working principle in the domain of Physics.
[8]For an example of such permutations see pp. [28] and [61], [62].
[9]LIOUVILLE'S theorem is the criterion for the equal possibility or equal probability of different state distributions.
[10]A happy term, but one not in vogue among English-speaking physicists.
[11]The identity of entropy with the logarithm of this state of probability
is established by showing that both are equal to the same expression. It seems an easy step from this derivation to BOLTZMANN'S definition of entropy as the "measure of the disorder of the motions in a system of mass points."
[SECTION C]
(1) Existence, Definition, Measure, Relations, Properties, and Scope of Irreversibility and Reversibility.