4.5 LIES

The apparent contradiction is.. A box containing two gases (N2 & 02) at equal temperature and pressure separated by a partition. When the partition is removed the original state of ORDER moves to a more DISORDERED state driven by the second law towards equilibrium of position. The entropy (IF entropy = measure of disorder) clearly increases BUT the heat equation ds = dQ/T = 0..!! What's going on.. simple ds = dQ/T is NOT a complete statement of entropy change. It only accounts for the natural tendency to equilibrium of MOMENTUM.. but not equilibrium of POSITION.. Both are required, its just that equilibrium of position is not often required in the measure so we don't need it. dQ/T makes thermodynamic calculations of entropy based on macro properties like pressure and temperature possible.

What is happening is the random motion of atoms causes any system to move to a state which more probable among all its other possible states. It does this simply because there are many more ways of being in disordered state than an ordered state. This is what Boltzmann's equation is all about.

(absolute entropy)  s = k.log(W)     so entropy change ds = s2 - s1
hence  ds = k.log (W2) - k.log(W1) = k.log(W2/W1)

Now W2/W1 = (final #num of microstates)/(initial #num of microstates)
So if we are dealing cards for instance..
A royal flush (RF) is an ordered state = low entropy

There are 7 RF's per suit so 28 per deck = (28 microstates)
There are 52C7 possible hands = 133784560 (microstates)

So W2/W1 = 28/133784560  BUT that = Probability of (RF)..
So the actual entropy change of dealing RF is
                             ds = k.log(Pr(RF))

It does not matter that we are only calculating ds for card dealing and not the cards themselves.. Not only does this tell us..
                    Entropy = Measure of Disorder.. it also gives meaning to the term..
                        Order = Improbability..

It is utterly false to say entropy is not a measure of disorder. By Appendix 5.1 of [The God Law] we may also say to pay the entropy cost of dealing a royal flush from a well shuffled deck is 1/Pr(RF)) = dealing 4.778 million hands (that's on average).