Epilogue

Summary

While it remains true that “entropy is not a localized, microscale phenomenon at which we can point, even in our imaginations, and say, ‘Look! There is entropy’” and that, “if we insist on trying to understand a subject in ways inconsistent with its nature, we will be disappointed,” the eight chapters of this guide have prepared us to give a constructive answer to the question “What is entropy?”

Any short description of entropy will necessarily be figurative. After all, one task of a figure of speech is to transfer a complex meaning from an extended description to a word or short phrase. In fact, we have already considered several figurative descriptions of entropy that are appropriate in special contexts: transformation content, disorder, uncertainty, spread in phase space, and missing information. Transformation content was Clausius’s way of referring to how the entropy function indicates the direction in which an isolated system may evolve. Spread in phase space, while appropriate for statistical systems, depends upon familiarity with the technical concept of phase space.

Disorder has long been a popular synonym for entropy. But recently order and disorder as describing low and high entropy systems have fallen into disfavor. This is because scientists have become fascinated with isolated systems that generate apparent order from apparent disorder. For instance, consider a thoroughly shaken bottle of water and olive oil. When left undisturbed, the water and olive oil begin to separate into distinct layers with the less dense olive oil on top. Yet even in this process the entropy of the oil–water system increases. Thus, while order and disorder are suggestive, they can mislead.