Blundell Thermal Physics · Problem 4.9

Temperature and the Boltzmann factor

Physics — Statistical Mechanics · boltzmann-distribution-computer-simulation

Problem

Write a computer program to reproduce the results in Example 4.2. For the case of

\mathcal{N} \gg 1

sites with initially one quantum per site, show that after many iterations you would expect there to be

N(n)

sites with

n

quanta, where

N(n) \approx 2^{-n}\mathcal{N}, \tag{4.38}

and explain why this is a Boltzmann distribution. Generalize your results for

\mathcal{Q} \gg 1

quanta distributed on

\mathcal{N} \gg 1

sites.