Who sees the future? Let us have free scope for all directions of research; away with dogmatism, either atomistic or anti-atomistic! - Ludwig Boltzmann

According to the second fundamental theorem... change has to take place in such a way that the total entropy of the particles increases. This means according to our present interpretation that nothing changes except that the probability of the overall state for all particles will get larger and larger.

[I]t is our main purpose not to limit our discussion to thermal equilibrium, but to explore the relationship of this probabilistic formulation to the second theorem of the mechanical theory of heat.

It can never be proved from the alone, that the minimum function H must always decrease. It can only be deduced from the laws of probability, that if the initial state is not specially arranged for a certain purpose, but haphazard governs freely, the probability that H decreases is always greater than that it increases. It is well known that the theory of probability is as exact as any other mathematical theory, if properly understood. If we make 6000 throws with dice, we cannot prove that we shall throw any particular number exactly 1000 times; but we can prove that the ratio of the number of throws in which that number turns up to the whole number of throws, approaches the more to 1/6 the oftener we throw.