As any good statistical physicist or cook can tell you, the chance
of this happening is effectively zero. If every one of n molecules
has an equal chance of moving up or down in the soup, or a 50% chance
of being found moving upward, the probability that at some instant
all n molecules will move upward in unison is given by the expression
(½)n. For the n = 1.7 x 1025 molecules in a half litre of soup,
this is an unimaginably small number.
Arthur Eddington expressed these probabilities vividly in 1928
in his book The Nature of the Physical World. Speaking of the mathematically
identical problem of the probability of finding all of the molecules
of a gas in one half of a container at the same time, he said:
"The reason why we ignore this chance may be seen by a
rather classical illustration. If I let my fingers wander idly over
the keys of a typewriter it might happen that my screed made an
intelligible sentence. If an army of monkeys were strumming on typewriters
they might write all the books in the British Museum. The chance
of their doing so is decidedly more favourable than the chance of
the molecules all moving to one half of the vessel."
It is true that, given enough time, the most unlikely events could
happen by chance. Order could come from molecular disorder spontaneously,
and an array of monkeys could type all the books in the British
Museum. Neither is worth waiting for in the real world.