Explaining Gibbsean phase space to second year students

A new approach to teaching introductory statistical physics is presented. We recommend making extensive use of the fact that even systems with a very few degrees of freedom may display chaotic behaviour. This permits a didactic ‘bottom-up’ approach, starting out with toy systems whose phase space may be depicted on a screen or blackboard, then proceeding to ever higher dimensions in Gibbsean phase space. 1. Propaedeutics for statistical physics Teaching introductory statistical physics is a tough but rewarding exercise. Rewarding, since statistical physics is arguably one of the most beautiful achievements in our science; and there are always some students alert enough to sense this. And tough, since as a rule the necessary mathematical tools are not ready by the time StatPhys must be introduced—not later than at the beginning of the second student year. The main didactic obstacles may be summed up as follows: • Classroom experiments not possible. Except for the familiar Brownian motion demonstrations it is simply not possible to show the molecules ‘at work’ as they create the macroscopic effects we measure in a thermodynamics lab. • Subject usually presented in a purely formal way. Due to the lack of demonstration experiments the efficient didactic double step of formal derivation–experimental corroboration is not feasible, leading to a predominance of formalism in StatPhys courses and texts. • Formalism rather abstract. The didactic problems are enhanced by the fact that the said formalism refers to an abstract, high-dimensional phase space that is difficult to visualize. These problems may be addressed by a teaching strategy combining the following elements: • Replace classroom experiments by simulation. Over the last few years this has become a well-established method for the visualization and statistical analysis of the motion of model particles. 0143-0807/05/020243+08$30.00 c © 2005 IOP Publishing Ltd Printed in the UK 243