Order and arrangement are not properties of individual particles,
but of collections of particles. (Try describing to someone the
"arrangement" of just one object.) The total energy of a mole of
gas molecules is 6.022 x 1023 times
the average energy of one molecule.
We can talk about the entropy of a mole of gas molecules, but it
is not legitimate to divide this by 6.022 x 1023
to obtain an "average molecular entropy."
The entropy depends on more than merely how many molecules are
present, multiplied by some intrinsic property of each molecule.
Entropy describes how the particles are arranged relative to one
another. It thus gives a sense to the flow of time. Even though
the mechanical motions of each particle are reversible in time,
the steady increase in "mixed-upness" of a large collection of particles
is not.
The second law of thermodynamics, as we have discussed it, states
that, in any isolated region of space, entropy always spontaneously
increases with time.
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The physicist Arthur Eddington turned this statement around and
said: "On the microscopic level, all of the laws of physics are
completely reversible in time, and positive and negative directions
in time are undefined.
On the macroscopic level, positive time is that sequence of events
in which the entropy or disorder within an isolated system increases."
By Eddington's statement the second law becomes, not a statement
about entropy, but a definition of positive time. This is why Eddington
characterized entropy as "Time's Arrow."
Regardless of which way your own philosophical bent leads you to
look at the second law, it does make one important connection: In
the real universe positive time and increasing entropy always go
together.
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