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.

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.