You may have learned elsewhere that entropy is a measure of disorder, or chaos, and that increasing entropy shows a tendency of an ordered system to become disordered. But consider the following:
A beaker of water and cracked-ice pieces of various sizes appears disordered. After all the ice has melted, the beaker of water looks more orderly. But the beaker of water has a higher entropy, not a lower entropy.
A container of oil and water that has been vigorously shaken looks quite disordered. But the oil and water soon separate to what appears to be a more orderly state. However, the separated oil and water actually have a higher entropy, not a lower entropy.
The free expansion of a gas into a vacuum starts with completely random moving molecules and ends with completely random moving molecules at the same average speed. There doesn’t seem to be any difference in how ordered or disordered these two states are, but the expanded gas has a higher entropy.
The difficulty is that “disorder” is not a technical term; it has no scientific definition. What seems disordered to one person may not to another. And are we talking about macroscopic disorder, such as the pieces of cracked ice in a beaker of water, or microscopic disorder?
Disorder is a metaphor for entropy, and we don’t want to imply that it’s never useful. But, all in all, it’s much more productive to think of entropy as a measure of the spread or dispersal of energy.