Ludwig Boltzmann Quotes

Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics.

Bring forward what is true. Write it so that it is clear. Defend it to your last breath.

Entropy derives from the Greek “conversion”, “mutation”, “evolution”, but also “confusion” and “shame” (this latter meaning one finds in the writings of Hippocrates in the form ).

Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se colorer d'une teinte rose uniforme et à partir de ce moment on aura beau agiter le vase, le vin et l'eau ne partaîtront plus pouvoir se séparer. Tout cela, Maxwell et Boltzmann l'ont expliqué, mais celui qui l'a vu plus nettement, dans un livre trop peu lu parce qu'il est difficile à lire, c'est Gibbs dans ses principes de la Mécanique Statistique. Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from that moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.

Available energy is the main object at stake in the struggle for existence and the evolution of the world.

The general struggle for existence of animate beings is not a struggle for raw materials – these, for organisms, are air, water and soil, all abundantly available – nor for energy which exists in plenty in any body in the form of heat, but a struggle for [negative] entropy, which becomes available through the transition of energy from the hot sun to the cold earth.

I don't believe I have ever invented a line of thinking, I have always taken one over from someone else. I have simply straightaway seized on it with enthusiasm for my work of clarification. That is how Boltzmann, Hertz, Schopenhauer, Frege, Russell, Kraus, Loos, Weininger, Spengler, Sraffa have influenced me.

We are certainly able to create temporary pockets of order in certain places and at certain times, if we feed in the right amounts of energy and effort from the outside. However it turns out that this local increase in order comes at the expense of a decrease in the amount of order in your body and in your immediate environment. As you reorder the files or make the ruler stand upright, for example, you are using energy – and some of this energy is lost as heat since you are effectively doing some exercise. And adding heat to your environment means that you are increasing the disorder in the air molecules around your body. In fact it is even worse than this – the disorder which you create as a by-product of your reordering of files or balancing of rulers will always be greater than the amount of order which you manage to create. In other words, the law is correct in that the overall disorder in the Universe increases. So although we humans can invent stories, build buildings, and can even create new lives by giving birth, each of these acts will actually destroy more order in the rest of the Universe than it can possibly create in the resulting book, building or baby. Depressing? Actually it was a physicist called Ludwig Boltzmann who came up with the pioneering insights into this effect of increasing disorder – and he ended up committing suicide in 1906 by hanging himself while on vacation.

In 1877 he published his paper “Probabilistic foundations of heat theory”, in which he formulated what Einstein later called the Boltzmann principle; the interpretation of the concept of entropy as a mathematically well-defined measure of what one can call the “disorder” of atoms, which had already appeared in his work of 1872, is here extended and becomes a general statement.

We note that occasionally the remark is made that what Carnot called heat was actually entropy, which is conserved in his cycle. Although it would be preposterous to say that Carnot discovered entropy, we may understand why his argument worked and why Clausius and Thomson were able to rescue his cycle and incorporate it in the new discipline. Essentially he saw that there was something that was conserved in reversible processes; this was not heat or caloric, however, but what was later called entropy.

For a long time the celebrated theory of Boscovich was the ideal of physicists. […] If this theory were to hold good for all phenomena, we should be still a long way off what Faust’s famulus hoped to attain, viz. to know everything. But the difficulty […] would be only a quantitative one; nature would be a difficult problem, but not a mystery for the human mind. […] this simple conception of Boscovich is refuted in every branch of science, the Theory of Gases not excepted. The assumption that the gas-molecules are aggregates of material points, in the sense of Boscovich, does not agree with facts.

Here Boltzmann is referring to the fact that an atom cannot be a simple object, as was amply known in his time from spectroscopy. It was the study of this structure that paved the way to the theory of elementary particles in the twentieth century. These are the bricks from which one builds atoms and may derive a force between atoms of the kind imagined by Boscovich.

heat “always shows a tendency to equalize temperature differences and therefore to pass from hotter to colder bodies” [15]. A

The conservation of energy in the atomic model found its final treatment in the hands of Hermann von Helmholtz (1821–94), who, like Mayer, started from physiological considerations, and about whom we spoke in detail in the previous chapter. In his fundamental work of 1847 [18] he explicitly introduced the concept of potential energy.

The consequences of Thomson’s Principle of Dissipation were elaborated by Hermann von Helmholtz, who two years later described the “heat death” of the universe, the consequence of the transformation of all energy into heat [14].

The First Law starts from the fact that in any physical system there are two kinds of energy (for simplicity, we ignore the possible presence of electric and magnetic fields), mechanical and thermal. Their sum may change because one performs work on the system or supplies heat to the system.

The First Law simply states that the change in total energy equals the work performed on, plus the heat supplied to, the system (measured in suitable units).

The Second Law indicates that not all the processes compatible with the First Law can actually occur. Whereas one can easily perform work to heat up the system, it is not always enough to supply heat to increase the mechanical energy. At least two heat sources at different temperatures are needed, as shown by Carnot’s argument (sometimes one of the sources may be naturally supplied by the environment). Essentially the Second Law states that heat can never pass from a colder to a warmer body without some other related change occurring at the same time (see also the next chapter). The new ideas were propagated in a rapid fashion thanks to the lively and elegant exposition by Thomson [17]. The conservation of energy in the atomic model found its final treatment in the hands of Hermann von Helmholtz (1821–94), who, like Mayer, started from physiological considerations, and about whom we spoke in detail in the previous chapter. In his fundamental work of 1847 [18] he explicitly introduced the concept of potential energy.

It was during his career as a military surgeon that he published his most celebrated essay on “The conservation of force”, where “force” had the meaning, then common, of “energy”. There is no doubt that this essay imparted a very great impulse to the problem of understanding the role and meaning of this basic principle of physics. In particular, Helmholtz clarified the assumptions that have to be made about a mechanical system in order to ensure that energy is conserved. As a result of his work the principle of conservation of energy became the unfailing guide to organizing physical facts and theories in a clear scheme.

In the description of matter as a collection of molecules instead of a continuum, questions related to reversibility are presented for the first time in the invention, almost as a joke, of what is now known as “Maxwell’s demon”.

he stressed that the main feature of science is economy of thought;

Thus, says Helmholtz [19], we do not try to construct machines that perform the thousands of acts typical of a man, but rather require that one machine performs a single act and replaces thousands of men.

The night of his birth marked the passage from Shrove Tuesday to Ash Wednesday and Boltzmann used to say that his birth date explained why his temper could suddenly change from great happiness to deep depression.

At first he did not realize what he had accomplished; he thought that he had remained within the boundaries of mechanics, that he was computing actual numbers of molecules, without realizing how much probability was involved.

Whenever he had to leave her, Boltzmann, who was tender-hearted, was not able to hold back his tears.

There is no mechanical impossibility, it is merely the fact that there are so many more possible positions of the various powder grains that will give a grey appearance, as compared to the much smaller number of configurations in which the grains are well ordered.

What we can do is to establish a bridge between the various levels in order to form a coherent picture; the whole of Boltzmann’s work is a masterpiece of this procedure, i.e. how to construct, starting from atoms, a description that explains everyday life.

Rather than probability, one can speak of a measure of the disorder of the atoms, because the equivalent disordered states (for a given macroscopic state) are very many and the probability that one of them occurs is extremely high. We shall discuss this paper in detail in Chapter 6.

About this unpleasant situation Boltzmann wrote: “I hate this continuous secret battle; I know much better how to integrate than how to intrigue.

There are hierarchies of structures, and new concepts arise at each level.

In the same paper Boltzmann was able to derive a proof of the irreversibility of macroscopic phenomena. It is the difference of scale between the objects that we observe in everyday life on the one hand, and molecules on the other hand, which explains this irreversibility through the laws of probability.

1.3 Restlessness

electricity and magnetism into a set of four elegant mathematical equations. On seeing them, Ludwig Boltzmann immediately recognised the magnitude of Maxwell’s achievement and could only quote Goethe in admiration: ‘Was it a God that wrote these signs?

The grandfather of this brilliant madness was Austrian physicist Ludwig Boltzmann, whose proof that gas molecules disperse in proportion to their temperature was foundational to all that followed. Boltzmann showed that molecular movement is simply determined by probability, which results in concentrations of molecules dispersing until they reach equilibrium with their environment. If you pour a potful of boiling water into a cold bath, hot water molecules spread out until they are evenly distributed and have slightly raised the overall bath temperature. Time cannot go backward for the same reason that boiling water can’t re-form in one corner of a cold bath and the dead cannot return to life: random probability will never re-concentrate those molecules back into their original form. The branch of physics pioneered by Boltzmann was called statistical mechanics, and it explained one of the fundamental laws of nature: the Second Law of Thermodynamics, also known as entropy.

The source of Rilke’s “eternal current” is nothing other than this. Appointed a university professor at just twenty-five years old; received at court by the emperor at the apex of his success; severely criticized by the majority of the academic world, which did not understand his ideas; always precariously balanced between enthusiasm and depression: the “dear sweet chubby one,” Ludwig Boltzmann, will end his life by hanging himself. He does so at Duino, near Trieste, while his wife and daughter are swimming in the Adriatic. The same Duino where, just a few years later, Rilke will write his Elegy.

Because the formula he derived for measuring the average number of bits needed to encode a piece of information looked almost exactly like Ludwig Boltzmann and Josiah Willard Gibbs’s formula for calculating entropy in thermodynamics. Here’s Shannon’s equation for calculating the size of any given piece of information: H = –Σi pi logb pi And here’s one way of stating Boltzmann’s equation for calculating the entropy of any given system: S = –kB Σi pi ln pi These two equations don’t just look similar; they’re effectively the same. Shortly after deriving his equation, Shannon pointed the similarity out to John von Neumann, then widely considered the world’s best mathematician. Von Neumann shrugged, suggesting that Shannon call his measure of the number of bits needed to carry a piece of information information entropy on the grounds that no one really understood thermodynamic entropy either.

Ludwig Boltzmann, one of the heroes of this story, put it this way: “It must be splendid to command millions of people in great national ventures, to lead a hundred thousand to victory in battle. But it seems to me greater still to discover fundamental truths in a very modest room with very modest means—truths that will still be foundations of human knowledge when the memory of these battles is painstakingly preserved only in the archives of the historian.

Ludwig Boltzmann had used statistics to explain how heat disperses as atoms and molecules collide. Planck found that only by applying the same statistics to oscillating electrons in the cavity resonator’s walls could he derive an equation that accurately matched what was observed.

Who sees the future? I am conscious of being only an individual struggling weakly against the stream of time. —Ludwig Boltzmann

Now up to the end of the eighteenth century, notably in the work of chemists, heat was treated as a substance, named caloric by the great French chemist Antoine Laurent Lavoisier (1743–1794), who made the first attempt to introduce the methods and concepts of physics laid down by Galileo and Newton into chemistry.

These are presumably the thoughts that made him restless.