A pedagogical approach to theBoltzmann factor through experimentsand simulations

The Boltzmann factor is the basis of a huge amount of thermodynamic andstatistical physics, both classical and quantum. It governs the behaviourof all systems in nature that are exchanging energy with their environment.To understand why the expression has this specific form involves a deepmathematical analysis, whose flowof logic is hard to see and is not at the level ofhigh school or college students’ preparation. We here present some experimentsand simulations aimed at directly deriving its mathematical expression andillustrating the fundamental concepts on which it is grounded. Experimentsuse easily available apparatuses, and simulations are developed in theNet-Logo environment that, besides having a user-friendly interface, allowsan easy interaction with the algorithm. The approach supplies pedagogicalsupport for the introduction of the Boltzmann factor at the undergraduate levelto students without a background in statistical mechanics.