The Boltzmann Distribution

2/22/01

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Table of Contents

The Boltzmann Distribution

Motivation

Outline

Definition

Definitions

To determine the most probable distribution (the equilibrium distribution) we must be able to calculate the number of configurations that lead to each of the possible distributions. 

Justification of formula for W

Thus, 

How do we find the max in a multi-variable function?

How do we find the max in f(x,y) subject to a constraint on possible values of x and y?

PPT Slide

PPT Slide

therefore

Likewise,

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So our new criteria are:

With two constraints, g=0 and h=0, 

Returning to the Boltzmann Distribution

This gives the criterion

Thus,

To eliminate A we use,

Undefended for now, I will assert ?=1/kT 

conclusion

Author: 

Email: mberry@usd.edu

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