Active Learning Approach for an Intuitive Understanding of the Boltzmann Distribution by Basic Computer Simulations

Abstract

The Boltzmann distribution lies at the heart of essentially all of statistical thermodynamics. In most textbooks, this distribution is introduced either ad hoc or it is mathematically derived by constrained entropy optimization using the method of Lagrange multipliers. Unfortunately, when students enroll in a statistical thermodynamics course, many are not familiar with this method from their prerequisite calculus courses. The recent availability of powerful computational devices for essentially all students provides an alternative way to explore the origin of qualitative and quantitative aspects of the Boltzmann distribution. Here we demonstrate a straightforward simulation approach to obtain an intuitive understanding of this distribution. We also make available concise and easily understandable computer programs in MATLAB and Python, providing an opportunity for an active learning experience of this fundamental law.