192-194] Irreversibility 167 



The analogy of the distribution of a pack of cards will help us to see 

 further into the problem presented by the entropy of a gas. In dealing 

 cards, it is just as likely that the dealer will have the thirteen trumps 

 as that he will have any other thirteen cards that we like to specify. The 

 occurrence of a hand composed of thirteen trumps might, however, be 

 justly regarded as a "coincidence," whereas the occurrence of any specified 

 hand in which the cards were more thoroughly mixed, could not reasonably 

 be so regarded. The explanation is that there are comparatively few ways in 

 which a hand which is all trumps can be dealt, but a great number in which 

 a mixed hand can be dealt. 



A similar remark applies to the result of putting cold water over a hot 

 fire. There are comparatively few ways in which the fire can get hotter, and 

 the water colder, but a great many ways in which the fire can impart 

 heat to the water a proposition which becomes obvious on looking at it 

 from the dynamical point of view of the generalised space. Speaking loosely, 

 it is just as likely that the water will freeze as that it will boil in any 

 specified way. There are, however, so many ways in which the water can 

 boil, all these ways being indistinguishable to us, that we can say that it 

 is practically certain that the water will boil. 



The increase of entropy, then, simply means the passage from a more 

 easily distinguishable state to a less easily distinguishable state, or, in 

 terms of the generalised space, from a less probable to a more probable 

 configuration. 



In reference to the generalised space, however, we saw that a decrease 

 of <) denoted the passage of a system from a rarer to a more common, or, if 

 we like, from a less probable to a more probable configuration. The theorem 

 of increasing entropy is, therefore, identical with the principle of decreasing 

 ), by the help of which we investigated the motion of a gas towards its steady 

 state. 



194. A reference to equation (397) shews that the entropy consists of 

 two parts, the former depending on the energy of the molecules of the gas, 

 and the latter on their positions. So far we have considered only variations 

 in the first term, resulting from inequalities in the temperature of the gas. 

 Similar remarks could, however, be made about the variations of the second 

 term, these denoting inequalities in the density of the gas. A single 

 illustration, suggested by Willard Gibbs*, will, perhaps, make clear what 

 is meant. 



If we put red and blue ink together in a vessel, and stir them up, 



common experience tells us that, if we assume the inks initially to differ in 



nothing more than colour, the result of stirring is a uniform violet ink. 



Here we have the passage from a more easily distinguishable to a less easily 



* Elementary Principles of Statistical Mechanics, p. 144. 



