Entropy as Time's Arrow
One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. This tells us that the right hand box of molecules happened before the left.
Caveats and Objections
There are some subtleties in the nature of entropy and other thermodynamic quantities, subtleties that we try to put into word pictures and sketches which sometimes oversimplify. In teaching thermodynamics, I have always tried to keep in mind the words of one of the great physics teachers of the mid-20th century, Mark Zemansky:
is as easy as a song:
You think you make it simpler
when you make it slightly wrong."
The diagrams above have generated a lively discussion, partly because of the use of order vs disorder in the conceptual introduction of entropy. It is typical for physicists to use this kind of introduction because it quickly introduces the concept of multiplicity in a visual, physical way with analogies in our common experience. Chemists, on the other hand, often protest this approach because in chemical applications order vs disorder doesn't communicate the needed ideas on the molecular level and can indeed be misleading. The very fact of differences of opinion on the use of order and disorder can itself be instructive.
The top diagram depicts time's arrow as pointing from order to disorder, but one must admit that the apparent tendency to move from order to disorder is not the most fundamental way to look at the top diagram. At ordinary temperatures, the internal energy of a gas would give the molecules high velocities, and it is evident that this orderly arrangement would be very rare because there are only a few ways to do it. If it occurred, it would be for a brief instant and then the molecules would move to some other configuration. The diagram at left depicts a more random or disordered configuration, but the key point is that there is a vast number of ways that such configurations could be achieved. So multiplicity is the key concept - molecular ensembles will spontaneously tend to evolve from configurations of lower multiplicity to configurations of greater multiplicity.
The bottom diagram is again a picture with which common experience immediately identifies - there are more ways to create a jumbled pile of bricks than a neatly stacked arrangement. Again, the idea of multiplicity is the key point. Objections to this kind of introduction to entropy come from the fact that the useful applications of entropy are thermodynamic ones and involve nature on the atomic and molecular scale. The ordered bricks vs the jumbled pile may be a useful introductory visualization, but if these two piles of bricks were at the same temperature, then the numerical value of the entropy would be almost identical for the two stacks. If the contributions to entropy involves the multiplicity of the ways that the vast number of molecules in the two stacks of bricks can be arranged, then the fact that the macroscopic orientations of the bricks is different is a negligible contribution to the total entropy. Entropy is a crucial microscopic concept for describing the thermodynamics of systems of molecules, and the assignment of entropy to macroscopic objects like bricks is of no apparent practical value except as an introductory visualization.