Modelling thermionic emission by using a two Level mechanical system

The Boltzmann factor is at the basis of a great amount of thermodynamic and statistical physics, both classical and quantum. It describes the behaviour of natural systems that exchange energy with the environment. However, why does the expression have that specific form? The Feynman Lectures on Physics justifies it heuristically by referencing to the "exponential atmosphere" example. Thermodynamics textbooks usually give a more or less complete explanation that mainly involves a mathematical analysis, where it is hard to see the logic flow. Moreover, the necessary mathematics is not at the level of high school or college students' preparation. Here we present an experiment and a simulation aimed at deriving the Boltzmann factor expression and illustrating the fundamental concepts and principles of statistical mechanics. Experiments and simulations are used in order to visualise the mechanisms involved; the experiments use easily available laboratory equipment, and simulations are developed in NetLogo, a software environment that, besides having a really friendly interface, allows the user to easily interact with the algorithm, as well as to modify it.