Ehrenfest’s Lottery — Time and Entropy Maximization


  • Henry S. Ashbaugh Tulane University


Successful teaching of the Second Law of Thermodynamics suffers from limited simple examples linking equilibrium to entropy maximization. I describe a thought experiment connecting entropy to a lottery that mixes marbles amongst a collection of urns. This mixing obeys diffusion-like dynamics. Equilibrium is achieved when the marble distribution is uniform and the entropy is maximized. I also show the ideal gas law results from the entropy change when the number of urns is increased.

Author Biography

Henry S. Ashbaugh, Tulane University

Henry S. Ashbaugh is an associate professor of chemical and biomolecular engineering at Tulane University. He holds chemical engineering degrees from North Carolina State University (B.S. ’92) and the University of Delaware (Ph.D. ’98). Hank joined Tulane after research appointments at Lund University in Sweden, Princeton University, and Los Alamos National Laboratory. His research interests are in the application of statistical thermodynamics and molecular simulations towards advancing self-assembly for understanding nanostructured materials.