Let the molecules of certain es behave as rigid bodies. The molecules of the gas and of the enclosing vessel move through the ether without loss of e… - Ludwig Boltzmann

The initial state in most cases is bound to be highly improbable and from it the system will always rapidly approach a more probable state until it finally reaches the most probable state, i.e., that of the heat equilibrium.

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.

Mr. Culverwell says that my theorem cannot be true because if it were true every atom of the universe would have the same average , and all energy would be dissipated. I find, on the contrary, that this argument only lends to confirm my theorem, which requires only that in the course of time the universe must tend to a state where the average vis viva of every atom is the same and all energy is dissipated, and that is indeed the case.