The Boltzmann Machine Model simulates a ping-pong ball moving around on two flat surfaces that are connected by a ramp. This ball is given occasional random "kicks" which cause the ball to move unpredictably.  Remarkably, this simple system is a macroscopic example of a two-level system* that obeys the Boltzmann distribution function. The Boltzmann distribution is typically associated with a microscopic system in contact with a heat bath; but in this case, the system is macroscopic and easy to visualize, and the random kicks serve the role of the heat bath. In Ref. 1, "Squiggle Balls" were used to produce the kicks for the Boltzmann Machine experiment, whereas in this simulation we use randomly generated velocities to produce the kicks. The advantage to using this simulation (as opposed to the experiment) is that parameters can be manipulated, and results can be obtained, much more quickly and easily.

The Boltzmann Machine Model was developed using the Easy Java/JavaScript Simulations (EjsS) modeling tool version 5.  It is distributed as a ready-to-run (compiled) Java archive.    Double clicking the ejs_fmu_BoltzmannMachine.jar file will run the program if Java is installed.  You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

*This is a "two-level" system in the sense that there are two different values of potential energy: the value on the top surface and the value on the bottom surface.

1. J. J. Prentis, American Journal of Physics 68, 1073 (2000).

This work was supported in part by NSF-TUES grant DUE-1140034.

Please note that this resource requires at least version 1.6 of Java.