The Word Travels

In 1865 Rudolf Clausius needed a name for a quantity he had been working with for more than a decade. He tried a plain name first — S, he wrote, could be called the transformation content of the body — and then explained, in the paper rather than leaving it to posterity, why he preferred Greek. Here in W. F. Magie’s 1935 translation:

since I think it is better to take the names of such quantities as these, which are important for science, from the ancient languages, so that they can be introduced without change into all the modern languages, I proposed to name the magnitude S the entropy of the body, from the Greek word ἡ τροπή, a transformation. I have intentionally formed the word entropy so as to be as similar as possible to the word energy, since both these quantities… are so nearly related to each other in their physical significance that a certain similarity in their names seemed to me advantageous.

Greek, so it would travel unchanged into every modern language. Shaped to rhyme with energy because the two belong together. And derived from τροπή, which means transformation. It is a small masterpiece of naming, and it worked. What Clausius did not design was how far it would go.

Clausius’s entropy is heat exchanged over temperature — a quantity of a body, with a thermometer in it. Ludwig Boltzmann read it microscopically: count the arrangements of molecules that look the same from outside, take the logarithm. Josiah Willard Gibbs replaced the count with a probability distribution. Same word, and a different kind of object under it. Nobody disputes that they connect.

Then, in 1948, Claude Shannon wrote down a measure of the uncertainty in a source of messages and called it entropy. His own account is on the record and undramatic. The form of H, he wrote in the paper, would be recognised as that of entropy as defined in certain formulations of statistical mechanics, and he pointed to Boltzmann’s H-theorem.

Notice what he was careful to say: the form. The form carried over; the use did not.

Clausius’s entropy is a state quantity, but what it keeps is a tally. He got it out of a transfer, heat exchanged divided by temperature, and the achievement was to find in that transfer a quantity belonging to the body alone: a state quantity whose content is transformation, whatever route was taken. His second law is about the tally’s direction, and the paper closes on it — the entropy of the universe tends toward a maximum. Left to itself, a system’s entropy rises.

Shannon’s use is about change too, and here the change is chosen. A sender writes variation into a carrier; the channel works because a medium can be put into distinguishable states. His scheme ends in a box marked destination, and sender and destination share a base — the code, and the statistics of the language. Against that shared base each arriving message is more or less expected. Shannon wrote of uncertainty and of choice; Myron Tribus, in 1961, supplied the word surprisal for the single message, and it fits. Entropy is then the surprise a source delivers on average: a property of the source, felt as the newness of what arrives, measured against the base the destination shares with the sender.

The transformation content of a body became the transformation content of a message — undergone in the one, chosen in the other. Whether it is one quantity is another matter.

This post is part of the conversations series. See also the reference entries on entropy and Shannon.

Photo: tsd_studio / Unsplash