FAR FROM EQUILIBRIUM, FOR 2500 YEARS

Ignis mutat res. Fire transforms matter; fire leads to chemical reactions, to processes such as melting and evaporation. Fire makes fuel burn and release heat. Out of all this common knowledge, nineteenth century science concentrated on the single fact that combustion produces heat and that heat may lead to an increase in volume; as a result, combustion produces work. Fire leads, therefore, to a new kind of machine, the heat engine, the technological innovation on which industrial society has been founded.
What is then the link between ‘heat’ and ‘work’? This question was at the origin of the formulation of the principle of energy conservation. Heat is of the same nature as energy. In the heat engine, heat is transferred into work but energy is conserved.
However, there was more. In 1811 Baron Jean-Joseph Fourier, the Prefect of Is`ere, won the prize of the
French Academy of Sciences for his mathematical description of the propagation of heat in solids. The result stated by Fourier was surprisingly simple and elegant: heat flow is proportional to the gradient of temperature.
It is remarkable that this simple law applies to matter, whether its state is solid, liquid or gaseous. Moreover, it remains valid whatever the chemical composition of the body, whether it is iron or gold. It is only thecoefficient of proportionality between the heat flow and the gradient of temperature that is specific to each substance.
Fourier’s law was the first example describing an irreversible process. There is a privileged direction of
time as heat flows according to Fourier’s law, from higher to lower temperature. This is in contrast with the laws of Newtonian dynamics in which the past and future play the same role (time enters only in Newton’s law through a second derivative, so Newton’s law is invariant in respect to time inversion). As already mentioned, it is the Second Law of thermodynamics that expresses the difference between ‘reversible’ and irreversible processes through the introduction of entropy. Irreversible processes produce entropy.
The history of the two principles of thermodynamics is a most curious one. Born in the middle of
technological questions, they acquired rapidly a cosmological status. Let us indeed state the two principles as formulated by Rudolph Clausius (1822–1888) in the year 1865:
 

The energy of the universe is constant.

The entropy of the universe approaches a maximum.

It was the first evolutionary formulation of cosmology. This was a revolutionary statement as the existence of irreversible processes (and therefore of entropy) conflicts with the time-reversible view of dynamics. Of course, classical dynamics has been superseded by quantum theory and relativity. However, this conflict remains because, in both quantum theory and relativity, the basic dynamical laws are time-reversible.
The traditional answer to this question is to emphasize that the systems considered in thermodynamics
are so complex (they contain a large number of interacting particles) that we are obliged to introduce
approximations. The Second Law of thermodynamics would have its roots in these approximations! Some authors go so far as to state that entropy is only the expression of our ignorance!
Here again the recent extension of thermodynamics to situations far-from-equilibrium is essential. As we mentioned already, irreversible processes lead then to new space–time structures. They therefore play a basic constructive role. No life would be possible without irreversible processes (see Chapter 19). It seems absurd to suggest that life would be the result of our approximations! We can therefore not deny the reality of entropy, the very essence of an arrow of time in nature. We are the children of evolution and not its progenitors.
Questions regarding the relation between entropy and dynamics have received great attention recently but they are far from simple. Not all dynamical processes require the concept of entropy. The motion of the Earth around the Sun is an example in which irreversibility (such as friction due to tides) can be ignored and the motion described by time symmetric equations. However, recent developments in nonlinear dynamics have shown that such systems are exceptions. Most systems exhibit chaos and irreversible behavior

(D. Kondepudi, I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, 2014)

Yes, the majority of systems exhibit irreversible, chaotic behavior (which does not mean random or confused https://ilchimicoscettico.blogspot.com/search/label/Caos). But this simple assumption seems to escape most people, especially among those who today are defined as "science" or "scientific community." And so we have heard talk of linear growth of measles cases in 2017 and of "exponential" COVID in 2020 (after all, an exponential on a logarithmic scale is a straight line) - and it still continues.

This makes me quote for the umpteenth time Lord Robert May with his words from 1989: "The message that seemed urgent to me more than ten years ago is even more true today: not only in biological research but also in the daily life of politics and economics things would be much better if it were understood that simple nonlinear systems do not necessarily possess simple dynamic properties"

But nothing doing: however urgent the message was in 1979 and in 1989 and even more urgent now, it continues to be fundamentally ignored. And it seems like something deeply ingrained in the majority of human beings, from time immemorial.

Only rereading it have I noticed the Heraclitean flavor of the incipit of the passage by Kondepudi and Prigogine. But after all, Heraclitus gave us the first formulation of the arrow of time in his own way, while the Eleatics considered time illusory. And not only. If we are indebted to a rooster to Asclepius and entropy to Carnot (https://ilchimicoscettico.blogspot.com/2022/11/entropia-in-uk-e-imparare-ad-essere.html), to Heraclitus we also owe the λόγος. Yet what did he write in his time?

Most people do not understand the very things they encounter, nor do they know them, even though they have received instruction about them, although it seems to them that they do.

It is good to report one of the notes by F. Fronterotta, editor of this edition of the Fragments:

The verb φρονέυω means in general "to reflect," "to reason" or even "to think," but in this case it seems to allude rather to a process of understanding or awareness, which most people cannot put into action, directed at objects and phenomena of ordinary and daily experience, presumably precisely those that they would have the capacity to understand if, as indicated by fragment 1 [1 DK; 1 Marc.], they paid attention to listening and to the teaching of "reasoning," which precisely reveals "everything according to its nature and saying how it is"

No, it is not possible to immerse oneself twice in the same river, yet for 2,500 years people continue to forget this simple evidence. This Heraclitean fragment, like others, comes from the Stromata of Clement of Alexandria and this provenance is nothing but the umpteenth sign of the intellectual strength of the Alexandrian fathers, who had to clash with dualist sects more or less Christianizing. These sects preached the ontological inferiority of a good part of human beings compared to the πνευµατικοi, the spiritual ones (https://ilchimicoscettico.blogspot.com/2021/01/divagazioni-antiche-tardo-antiche-etc.html). Which, when you think about it, mutatis mutandis, is one of the most widespread ideologies in this century: the instances aimed at depriving non-conformists of constitutional rights we have seen well and the infinite invective against functional or returning illiterates by those who "read" or "have an education". But in the Heraclitean fragment there is no talk of reading or studying: φρονέυω, precisely, which is quite another thing.