Maximizing the Lagrangian

Highlights of the activity

1. Students are broken into small groups and asked to maximize a Lagrangian describing an arbitrary statistical mechanical system.
2. Students will maximize the Lagrangian to derive additional information about the probability for any arbitrary state in the system as well as the partition function.

Reasons to spend class time on the activity

For many students, this activity may be the first time they are seeing a Lagrangian. This activity demonstrates the usefulness of the method of Lagrange Multipliers to acquire additional information about a system. This activity also provides students the opportunity to manipulate the fairness function. Having small groups perform this exercise will also transition into defining the partition function and how it's notation is used to simplify expressions.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version