Ludwig Boltzmann Quotes

[I]t is possible to calculate the state of the equilibrium of heat by finding the probability of the different possible states of the system.

It is clear that every single uniform state distribution which establishes itself after a certain time given a defined initial state is equally as probable as every single nonuniform state distribution, comparable to the situation in the game of Lotto where every single quintet is as improbable as the quintet 12345. The higher probability that the state distribution becomes uniform with time arises only because there are far more uniform than nonuniform state distributions... It is even possible to calculate the probabilities from the relationships of the number of different state distributions. This approach would perhaps lead to an interesting method for the calculation of the equilibrium of heat.

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

Wie ohnmächtig der Einzelne gegen Zeitströmungen bleibt, ist mir bewusst. Um aber doch, was in meinen Kräften steht, dazu beizutragen, dass, wenn man wieder zur Gastheorie zurückgreift, nicht allzuviel noch einmal entdeckt werden muss, nahm ich in das vorliegende Buch nun auch die schwierigsten, dem Missverständnisse am meisten ausgesetzten Theile der Gastheorie auf und versuchte davon wenigstens in den Grundlinien eine möglichst leicht verständliche Darstellung zu geben.

I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that, when the theory of gases is again revived, not too much will have to be rediscovered. Thus in this book [this Part] I will now include the parts that are the most difficult and most subject to misunderstanding, and give (at least in outline) the most easily understood exposition of them.

If this assumption were correct, our world would return more and more to ; but because the whole universe is so great, it might be probable that at some future time some other world might deviate as far from thermal equilibrium as our world does at present. Then the aforementioned H-curve would form a representation of what takes place in the universe. The summits of the curve would represent the worlds where visible motion and life exist.

But if we ask why this state is not yet reached, we again come to a "Salisburian mystery."
I will conclude this paper with an idea of my old assistant, Dr. Schuetz.
We assume that the whole universe is, and rests for ever, in thermal equilibrium. The probability that one (only one) part of the universe is in a certain state, is the smaller the further this state is from thermal equilibrium; but this probability is greater, the greater is the universe itself. If we assume the universe great enough, we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please. We can also make the probability great that, though the whole universe is in thermal equilibrium, our world is in its present slate. It may be said that the world is so far from thermal equilibrium that we cannot imagine the improbability of such a state. But can we imagine, on the other side, how small a part of the whole universe this world is? Assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.

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.

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.

<small>Ref: Boltzmann, "Bemerkungen über einige Probleme der mechanischen Warmetheorie," Sitz. ber. der k. Wien. Acad. vol. lxxv. 1877</small>

I pointed out in the second part of my paper... that my Minimum Theorem, as well as the so-called , are only theorems of probability. The Second Law can never be proved mathematically by means of the equations of dynamics alone.

It may be objected that the above is nothing more than a series of imperfectly proved hypotheses. But granting its improbability, it suffices that this explanation is not impossible. For then I have shown that the problem is not insoluble, and nature will have found a better solution than mine.

Moreover, it is doubtful whether emission of rays of visible light takes place in simple gases without chemical action. Certainly the light of sodium and that of Gassiot's tubes do not come from gases whose molecules are in thermal equilibrium.

If the ether be an external medium which flows freely through the gas, we might find a difficulty in explaining how it is that the source of radiant heat seems to be in the energy of the gas itself. But I still think it possible that the source of energy of the electric vibrations caused by the impact of two gas molecules in the surrounding ether, may be in the progressive and rotatory energy of the molecule. If the electric states of two molecules differ in their motions of approach and separation, the energy of progressive motion may be transformed into electric energy.

The possibility of the transference of energy being so gradual cannot be denied, if we also attribute to the ether so little friction that the Earth is not sensibly retarded by moving through it for many hundreds of years.