Quotes from Carlo Cercignani

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 ).

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.

1.3 Restlessness

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.

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.

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.

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).

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;

These are presumably the thoughts that made him restless.

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.

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.

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.

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.

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.

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.

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

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.

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.