Exploring Thermodynamics with Billiards

Tim Chumley explains the connections between random billiards and
the science of heat and energy transfer. If you've ever played
billiards or pool, you've used your intuition and some mental
geometry to plan your shots. Mathematicians have gone a step
further, using these games as inspiration for new mathematical
problems. Starting from the simple theoretical setup of a single
ball bouncing around in an enclosed region, the possibilities are
endless. For instance, if the region is shaped like a stadium (a
rectangle with semicircles on opposite sides), and several balls
start moving with nearly the same velocity and position, their
paths in the region soon differ wildly: chaos. Mathematical
billiards even have connections to thermodynamics, the branch of
physics dealing with heat, temperature, and energy transfer.