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Boltzmann Machine Model
written by Larry Engelhardt and Marie Lopez Puerto
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.
1 source code document is available
Subjects Levels Resource Types
Thermo & Stat Mech
- Ensembles
= Boltzmann Distribution
- Probability
= Random Walks
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Interactive Simulation
= Lecture/Presentation
Material Category Lab Software Type Ratings
- Software Exchange
- Simulation
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Intended Users:
Access Rights:
Free access
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Larry Engelhardt
Record Cloner:
Metadata instance created August 1, 2014 by Wolfgang Christian
Record Updated:
March 22, 2015 by Wolfgang Christian
Last Update
when Cataloged:
August 1, 2014
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Record Link
AIP Format
L. Engelhardt and M. Puerto, Computer Program BOLTZMANN MACHINE MODEL (2014), WWW Document, (
L. Engelhardt and M. Puerto, Computer Program BOLTZMANN MACHINE MODEL (2014), <>.
APA Format
Engelhardt, L., & Puerto, M. (2014). Boltzmann Machine Model [Computer software]. Retrieved April 25, 2017, from
Chicago Format
Engelhardt, Larry, and Marie Lopez Puerto. "Boltzmann Machine Model." (accessed 25 April 2017).
MLA Format
Engelhardt, Larry, and Marie Lopez Puerto. Boltzmann Machine Model. Computer software. 2014. Java 1.6. 25 Apr. 2017 <>.
BibTeX Export Format
@misc{ Author = "Larry Engelhardt and Marie Lopez Puerto", Title = {Boltzmann Machine Model}, Month = {August}, Year = {2014} }
Refer Export Format

%A Larry Engelhardt
%A Marie Lopez Puerto
%T Boltzmann Machine Model
%D August 1, 2014
%O application/java

EndNote Export Format

%0 Computer Program
%A Engelhardt, Larry
%A Puerto, Marie Lopez
%D August 1, 2014
%T Boltzmann Machine Model
%8 August 1, 2014

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Boltzmann Machine Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Boltzmann Machine Model.

relation by Wolfgang Christian

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