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?
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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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