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Students as molecules: Instructor's Guide

Main Ideas

Students randomly diffuse around the room and compute the entropy at each step.

Estimated Time: 15-30 minutes

Props/Equipment

• Student calculators
• One die per student (or coins)

Activity: Introduction

Begin by explaining the rules:

1. All students start at one table.

2. When instructed, each student rolls a die (or flips a coin). Based on that result, they either move or not. You can pick a meaning for each result, e.g. heads you move to a higher-numbered table, tails you move to a lower-numbered table. If you at the bottom, you can't go down and must stay put.

3. Once everyone has moved, each table must compute their own contribution to the entropy according to the formula: $$S = -k\sum P \ln P$$ The probability for each table is given by the fraction of the class that is at that table. The instructor writes these on the board and a student adds them up using a calculator.

4. Return to step 2 until enough steps have passed for students to see a trend.

Activity: Student Conversations

* Students will wonder what happens to $P\ln P$ when $P=0$.

Activity: Wrap-up

Discuss how maximizing entropy requires distributing the students equally among the tables, and how that happens naturally. Also how entropy generally increases, but does sometimes drop down. It just doesn't decrease very often, and the size of the decreases drops (fractionally) as the numbers get large.

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