# Second law of thermodynamics

The famous c.1990 cartoon by Sidney Harris, showing a grandfather reading to his grandson a book titled Facts of Life, wherein the "second law of thermodynamics" is one of the first facts.[1]

In thermodynamics, second law of thermodynamics (TR:5) (LH:4) (TL:9), aka “second main principle” (Clausius, 1865) or “second law”, when used in context[2], refers to []

## Overview

In 1854 to 1862, Rudolf Clausius, building on William Thomson (May 1854) and Sadi Carnot (1824), formulated the characteristic functions (#10 to #12), of what he was then calling the “second main principle” in the mechanical theory of heat, as a way to upgrade the Carnot cycle model, wherein heat, then defined as caloric particles, was defined as being conserved.

In the new model, instead of heat being conserved, at the end of each cycle, there was now a new value of "uncompensated transformation", symbol N, that accounted for the "irreversible" nature of heat-transforming-into-work, aka positive transformations, and work-transforming-into-heat, aka negative transformations, and the end of one heat engine work cycle. The value of this N, at the end of all the cycles, is what Clausius eventually called "entropy increase".

Because Clausius could not define this "N" value exactly, i.e. using an equals sign "=", he had to resort to a greater than or equals to sign "≥", and conclude with the fact that "N" would always be positive, aka the entropy of any body in the universe is always a positive value (Lewis, 1923), and that at the end of any cyclical process, the value of "N" would be at its "maximum value". This was a way of saying that although we could not find this value "N" exactly, because it had to do with the "work" the molecules of the system do on each other, which would be too difficult to measure, we could at least conclude that it would have a maximum value at he end of the process, which we could calculate.

All of this logic, which seems to have been lost to modern ears, became truncated into the term "maximum entropy", which presently has so much confused meaning attached to it, that it is nearly abysmal.

### Uncompensated transformations | Tend to maximum

In 1862, Clausius gives the following, aka characteristic function #12:

${\displaystyle \int {\frac {\delta Q}{T}}\geqq 0}$

which he says is the algebraic sum of the of all "positive transformations" (TR:5)[3] and "negative transformations" (TR:5)[4], occurring in a cyclical process, which can only be positive (Clausius, 1862).[5] This "can only be positive" (Clausius, 1862) became "tends to a maximum" (Clausius, 1865), as follows:

Clausius (1862) Clausius (1865) Planck (1908) Shannon (1949)
Statement “The sum of the values of "uncompensated transformations" of any cyclically transforming system in the universe tends to a maximum positive value.”
Rudolf Clausius (1862), Mechanical Theory of Heat (pg. #)
“The entropy of the universe tends to a maximum.”[6]
Rudolf Clausius (1865), Mechanical Theory of Heat (pg. 365) [7]
“The disorder of the universe tends to a maximum.”
Max Planck (1908), Publication (see: Planck entropy)[8]
“The information content of the universe tends to a maximum.”
Claude Shannon (1949), Mathematical Theory of Communication
Version Original; Correct Short; but too-packed Agenda-based; Incorrect Joke-based; Very-incorrect

The phrase "tends towards a maximum" is a restatement of his 1862 more exacting description of how the value of "uncompensated transformations" (TR:18)[9] (Clausius, 1862) can "only be positive" at the end of the cycle of operations. The cycle here being the "Clausius cycle", as contracted to the "Carnot cycle", which it was replacing or upgrading.

#### Confusables

Note: we also have shown two incorrect restatements, namely that of Planck (1908) and Shannon (1949), of the second law, which have grown to become falsely assume as true, owing to general cultural scientific ignorance. The 1908 "Planck entropy" model equates entropy to disorder. The 1949 "Shannon entropy" model, which equates entropy to information and bits.

### Entropy | Coining

The following is the original 24 Apr 1865 coining of entropy by Clausius, the 1867 Thomas Hirst English translation, and a direct Google translations:

Clausius (24 Apr 1865) Hirst (1867) Google (66AE)
Sucht man für S einen bezeichnenden Namen, so könnte man, ähnlich wie von der Grosse U gesagt ist, sie sei der Wärmennd Werkinhalt des Körpers, von der Grosse S sagen , sie sei der Verwandlungsinhalt des Körpers. Da ich es aber für besser halte, die Namen derartiger für die Wissenschaft wichtiger Grossen aus den alten Sprachen zu entnehmen, damit sie unverändert in allen neuen Sprachen angewandt werden können, so schlage ich vor, die Grosse S nach dem griechischen Worte η τροπή, die Verwandlung, die Entropie des Körpers zu nennen. Das Wort Entropie habe ich absichtlich dem Worte Energie möglichst ähnlich gebildet, denn die beiden Grossen, welche durch diese Worte benannt werden sollen, sind ihren physikalischen Bedeutungen nach einander so nahe verwandt, dass eine gewisse Gleichartigkeit in der Benennung mir zweckmnssig zu sein scheint. We might call S the transformation content of the body, just as we termed the magnitude U its thermal and ergonal content. But as I hold it to be better terms for important magnitudes from the ancient languages, so that they may be adopted unchanged in all modern languages, I propose to call the magnitude S the entropy of the body, from the Greek word τροπή, transformation. I have intentionally formed the word entropy so as to be as similar as possible to the word energy; for the two magnitudes to be denoted by these words are so nearly allied their physical meanings, that a certain similarity in designation appears to be desirable. If one looks for a descriptive name for S, one could say of the capital S, similar to what is said of the capital U that it is the body's warming content, that it is the transformation content of the body. But since I think it is better to take the names of such greats for science from the ancient languages so that they can be used unchanged in all new languages, I propose to use the capital S after the Greek word η τροπή, the transformation [change, metamorphosis], to call the entropy of the body. I intentionally formed the word entropy as similar as possible to the word energy, because the two greats which these words are supposed to name are so closely related in terms of their physical meanings that a certain similarity in naming seems to me to be useful.

Here, to note, Clausius has "packed" about 15-years worth of conceptual development into two simplified words: entropy and entropy. The reason, accordingly, why thermodynamics is so confused, for most, presently, is that these 15-years have never fully been unpacked.