reading memos and the arrow of time

At the suggestion of my pedagogy mentor Sanjoy Mahajan (MIT), I assign reading memos, to be turned in before the class in which I expect the reading to be done. This encourages the students to do the reading (I give a small fraction of the grade for doing the memos), and it also gives me some exceedingly insightful feedback about what works and what doesn't in the book I am using (Chabay & Sherwood).

In Chapter 11 (this week's chapter), the book makes the requisite notes about the increase in entropy possibly having something to do with the advance of time, a subject I avoid for its capability of generating enormous quantities of speculation. In the reading memos, one of my students (John Morrow) asked:

A closed system will tend toward maximum entropy. Is it possible for it to reach maximum entropy before the rest of the universe? And if so wouldn't that imply that time would stop for the closed system?

Beautiful question! This either throws doubt on that whole crazy idea, or else implies that all systems that have or perceive time must be out of equilibrium? Insane! But of course that would be some of that speculation I abhor.