What is the simplest definition of “entropy”?

The simplest definition of entropy that still retains some precision is: “the degree to which a system is unavailable to produce work.”

The more a system is able to produce work, the lower the entropy. If the system is no longer able to produce work, entropy is maximum.

The problem with this definition is that it configures entropy as the measure of a deficiency, and this makes the concept difficult to understand. For this reason, a second, simpler (but often misleading) definition is sometimes used that qualifies entropy as “the measure of the degree of disorder.”

The problem is that disorder in physics is not the same thing we normally think of.

Take for example a bag of marbles; we can say that it is orderly because the marbles all fit together. If we magically remove the bag, the marbles fall on the floor and scatter. At this point they are all disordered and entropy has increased.

However, let’s take the same marbles in the same “disorder” configuration and put them in a stable orbit around the earth. Give them enough time, and the gravitational attraction between the marbles will put them back together again. By the time they are all back together in a configuration similar to the one they originally had in the bag, the entropy will have increased, even…