Teaching the heat transfer law using a stochastic toy model

In this paper we present a simple stochastic toy model playable with dice, coins and tokens, meant to represent the system composed of a conducting bar between two heat reservoirs. The toy model is meant to be used in the context of a computational approach to teaching thermal physics to undergraduates, and allows one to highlight step by step the mechanism by which deterministic differential equations for macroscopic quantities can arise from underlying microscopic processes which are inherently random. Since this mechanism crucially requires the passage to the thermodynamic limit, in order to test it on their own students are required to code and perform numerical simulations of the toy model system with an increasingly large number of elements. From the point of view of training students with programming skills, the toy model offers a suitable ground for an early activity, since the simulation of a game they can actually perform is expected to produce less cognitive load than the simulation of more abstract problems and equations, allowing students to concentrate on learning the basics of programming.