## Monday, May 7, 2012

### What is a good description for entropy?

"Insight into Entropy," by Daniel F. Styer, is a nice paper that appeared in the American Journal of Physics in 2000. In the paper, he argues for a qualitative explanation of entropy that involves two ideas: disorder and freedom.

Entropy as disorder is a common analogy given to students who are learning about thermodynamics, but Styer provides several arguments for why this qualitative description fails to adequately explain the idea. One such argument involves a glass of shredded and broken ice. Despite the fact that the ice has been shattered into many pieces, the entropy of the bowl of ice is less than that of an identical bowl filled with water. The water may seem to be more ordered because it is homogeneous, but it does not possess a lower entropy.

Styer's idea of entropy as freedom attempts to explain how systems can possess multiple classes of states (commonly known as macrostates) and how entropy limits the microscopic details of each class. In the game of poker, the probability of getting a royal flush is identical to any other five-card selection without replacement. However, the number of configurations that form a royal flush is extremely small, so the entropy of the class of hands forming a royal flush is low. This very low entropy class of poker hands restricts the possible configurations of the microstate—the description of what five cards are in one's hand—and completes the analogy with freedom. High entropy macrostates have greater freedom in choosing their microstate by having a larger number of microstates to choose from; low entropy macrostates (royal flushes, for example) have less freedom.

Styer does propose retaining the "entropy as disorder" description by suggesting that both the freedom and disorder analogies be presented simultaneously to negate any emotions commonly associated with either word. His example of such an analogy goes as "For macrostates of high entropy, the system has the freedom to choose one of a large number of microstates, and the bulk of such microstates are microscopically disordered."

Finally, on a different train of though: teaching ideas by analogy apparently must be done with sensitivity to the common emotions associated with a word. I've never considered this idea before, but will surely be mindful of it in the future.