Entropy and Disorder?
I've often read that thermodynamic entropy is some measure of disorder, so that tyding up our rooms means working against the second law of thermodynamics. For example, in section 9.3 of his book Space, Time and Quanta, Robert Mills demonstrates that if we put 10^20 toys back on the shelf, that decreases the total cosmic entropy by 0.02 J/K. He then suggests that this doesn't actually violate the second law because in the process of putting back the toys we use up energy and thereby increase total entropy by much more than 0.02 J/K.
I don't like saying that physicists are wrong when they do physics (as opposed to when they do philosophy), but this just can't be right. If entropy is a well-defined physical quantity, it can't depend on what we happen to find orderly (toys on the shelf) or not (toys scattered on the floor). Without some more or less unnatural clarification of what is meant by 'disorder', there is probably no connection at all between thermodynamic entropy and disorder. And such a clarification will certainly not count toys on the shelf as being more orderly than toys on the floor.
I guess it also won't count a state of two gases floating around separated in a box as being more orderly than the state where they are mixed. For what has this difference got to do with temperature and energy? This also shows that the mere fact that some arbitrary macroscopic property (or distribution of the property) is realisable microphysically in more different ways than others can't have much to do with entropy. Otherwise the difference inentropy between two systems will have all kinds of different values depending on which macroscopic properties we focus on. For example, there are many microphysical possibilities for my brain to have the volume and temperature it has, but there are far less possibilities for it to play the functional role that it plays.
So if you write a pop science text on entropy, please don't pretend that it can be explained in terms of order and disorder or the number of microphysical realisations of macroscopic states.