Tuesday, 16 September 2014

What is the definition of entropy?

Having recently blogged on the subject:


I feel that it would be helpful for readers to have a clearer definition of entropy.

Luckily, one already exists, in Three Men in a Boat by Jerome K Jerome:

I do not wish to be insulting, but I firmly believe that if you took an average tow-line, and stretched it out straight across the middle of a field, and then turned your back on it for thirty seconds, that, when you looked round again, you would find that it had got itself altogether in a heap in the middle of the field, and had twisted itself up, and tied itself into knots, and lost its two ends, and become all loops; and it would take you a good half-hour, sitting down there on the grass and swearing all the while, to disentangle it again.
That is my opinion of tow-lines in general.  Of course, there may be honourable exceptions; I do not say that there are not.  There may be tow-lines that are a credit to their profession—conscientious, respectable tow-lines—tow-lines that do not imagine they are crochet-work, and try to knit themselves up into antimacassars the instant they are left to themselves.  I say there may be such tow-lines; I sincerely hope there are.  But I have not met with them.
This tow-line I had taken in myself just before we had got to the lock.  I would not let Harris touch it, because he is careless.  I had looped it round slowly and cautiously, and tied it up in the middle, and folded it in two, and laid it down gently at the bottom of the boat.  Harris had lifted it up scientifically, and had put it into George’s hand.  George had taken it firmly, and held it away from him, and had begun to unravel it as if he were taking the swaddling clothes off a new-born infant; and, before he had unwound a dozen yards, the thing was more like a badly-made door-mat than anything else.
A modern equivalent can be observed with the wires attached to those little earphone things that you use for listening to audio devices such as small radios, mobile phones, iPods and the like.


  1. I'm attached to the statistical mechanics definition having to do with the logarithm of the number of microstates corresponding to a given macrostate. But it's far too late to be able to get people to restrict themselves to that usage.

  2. @Bonald - Ah, I see you prefer the PG Wodehousian definition...

  3. @Bonald - You might be interested by a paper in Journal of Irreproducible Results from about 1991 - the title more or less tells you its approach:

    "An Estimation of Time Remaining Until the Heat Death of the Universe: A Messy Desk as a Model for Entropy"

    Quantitative observations of how quickly a desk gets itself messy were extrapolated to calculate the time left before the end of all things.

  4. Although your example is humorous I've come to the conclusion that the tendency for things to become tangled is some sort of basic mechanism at work in nature. If something can get tangled, it will, and I'm not joking!

  5. I have been meaning for some time to set up a video camera to record a box of unattended network cables over a period of several months. But perhaps entanglement is affected by the presence of an observer.

  6. @Crosbie - "perhaps entanglement is affected by the presence of an observer"

    Jerome K Jerome wrote about the effect of an observer too. From TMiaB:

    We put the kettle on to boil, up in the nose of the boat, and went down to the stern and pretended to take no notice of it, but set to work to get the other things out.

    That is the only way to get a kettle to boil up the river. If it sees that you are waiting for it and are anxious, it will never even sing. You have to go away and begin your meal, as if you were not going to have any tea at all. You must not even look round at it. Then you will soon hear it sputtering away, mad to be made into tea.

    It is a good plan, too, if you are in a great hurry, to talk very loudly to each other about how you don’t need any tea, and are not going to have any. You get near the kettle, so that it can overhear you, and then you shout out, “I don’t want any tea; do you, George?” to which George shouts back, “Oh, no, I don’t like tea; we’ll have lemonade instead—tea’s so indigestible.” Upon which the kettle boils over, and puts the stove out.

    We adopted this harmless bit of trickery, and the result was that, by the time everything else was ready, the tea was waiting.