Entropy: the "mathematical spook" and "ghostly quantity" of physics and thermodynamics.

“If stuff is at the absolute temperature and we give the small amount of heat to it, we say that we give it the entropy . Engineers seem to have great difficulty in understand why we introduce the notion of this ghostly quantity, but they must get accustomed to it.”

“It seems necessary in a book dealing with the application of the temperature-entropy diagram to discuss briefly that ‘ghostly quantity’, entropy, although I do not intend to give any new definition of a function already too variously defined, but rather to pick out such of the present ones as are correct.”

“This ‘ghostly quantity’, as Professor Perry calls it, is not perceptible by the senses, and cannot be measured directly by any gauge or meter. It is, nevertheless, a very convenient term of expression, and entropy-temperature diagrams are very instructive and very useful.”

“I should like to ask Professor Max Planck whether the view he expresses that ‘nature never undertakes any change unless her interests are served by an increase of entropy’ is to be taken with or without any particular reservation or with any special interpretation of ‘her interests’. My thermodynamic ideas are somewhat old-fashioned—viz., that there is invariably a dissipation of energy or loss of availability of energy due to imperfect or total want of reversibility in natural processes. This entirely agrees in effect with the way of expressing things in terms of increase of ‘entropy’, although that subtle quantity is certainly ‘ghostly’, and is somewhat too evasive to be regarded as a physical state even though it be a function of the physical state referred to a standard state. But the question is how the interests of Nature are served by imperfect reversibility? Professor Planck’s words suggest a choice on Nature’s part, as if Nature had any choice. Goethe said god himself could not alter the course of Nature. That was truly scientific. Then, again, what are to be considered the interests of Nature? Are we to take exactly things exactly as we find them, and define the interests in that way? If so, it carries us no further. Or is there a theorem of greatest entropy, showing how any variation from the proper course of Nature would tend to reduce the rate of increase of the entropy?”

“Whether entropy has any ‘ghostly’ attributes, is a question I will not open, but I am for the present quite content to know that it is a quantity which can be measured without ambiguity.”

“We have found that practice with blackboards leads to the most exact quantitative and practical knowledge of what goes on in heat engines. But the student must really state the answers as to heat and work exactly, the scales to which energies are represented being familiarly known. After a little practice, the ghostly quantity entropy gets to be as well known as electrical potential now is to experimenters—in 1868 it was merely a mathematical expression to most students, just as entropy now must remain to anybody who will not experiment.”

“Entropy is what someone has called a ‘ghostly quantity’, and it is so intimately connected with mathematics that it cannot be divorced from it.”

“Entropy is a shadowy kind of concept, difficult to grasp … but again, we may point out that, the reader who would extend the notion of mechanism into life simply must grasp it.”

“In those days I was essentially the only theoretical physicist there, whence things were not so easy for me, because I started mentioning entropy, but this was not quite fashionable, since it was regarded as a mathematical spook.”