Boltzmann Distribution from a Microcanonical Ensemble Model

written by
Larry Engelhardt and
Norman Chonacky

The Boltzmann Distribution From A Microcanonical Ensemble Model allows students and instructors to explore why the Boltzmann distribution has its characteristic exponential shape. In this model, particles have only one degree of freedom–the energy to move in one dimension. Further, the density of accessible states is chosen to be uniform –i.e. each state is equally probable. Starting with a system of N=2 particles, you are able to generate simple empirical results for the distribution of energies among the individual particles. Then you can observe how this distribution changes with increasing N, gradually approaching the Boltzmann distribution.

The Boltzmann Distribution From A Microcanonical Ensemble Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_fmu_BoltzmannDistribution_PartitioningEnergy.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.

Please note that this resource requires
at least version 1.5 of
Java.

Discrete Boltzmann Distribution Model
A discrete version of the Microcanonical Boltzmann Distribution Model, which partitions energy as discrete quanta rather than allowing the energy to be distribute continuously. download 1344kb .jar
Last Modified: August 4, 2014
previous versions

Boltzmann Distribution from a Microcanonical Ensemble Source Code
The source code zip archive contains an EJS-XML representation of the Boltzmann Distribution from a Microcanonical Ensemble Model. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 7kb .zip
Last Modified: November 22, 2011

Discrete Boltzmann Distribution Source Code
The source code zip archive contains an EJS-XML representation of the Discrete Boltzmann Distribution Model. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 8kb .zip
Last Modified: August 4, 2014

<a href="http://www.compadre.org/OSP/items/detail.cfm?ID=11563">Engelhardt, Larry, and Norman Chonacky. "Boltzmann Distribution from a Microcanonical Ensemble Model."</a>

L. Engelhardt and N. Chonacky, Computer Program BOLTZMANN DISTRIBUTION FROM A MICROCANONICAL ENSEMBLE MODEL (2011), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483).

L. Engelhardt and N. Chonacky, Computer Program BOLTZMANN DISTRIBUTION FROM A MICROCANONICAL ENSEMBLE MODEL (2011), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483>.

Engelhardt, L., & Chonacky, N. (2011). Boltzmann Distribution from a Microcanonical Ensemble Model [Computer software]. Retrieved May 6, 2016, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483

Engelhardt, Larry, and Norman Chonacky. "Boltzmann Distribution from a Microcanonical Ensemble Model." http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483 (accessed 6 May 2016).

Engelhardt, Larry, and Norman Chonacky. Boltzmann Distribution from a Microcanonical Ensemble Model. Computer software. 2011. Java 1.5. 6 May 2016 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483>.

@misc{
Author = "Larry Engelhardt and Norman Chonacky",
Title = {Boltzmann Distribution from a Microcanonical Ensemble Model},
Month = {October},
Year = {2011}
}

%A Larry Engelhardt %A Norman Chonacky %T Boltzmann Distribution from a Microcanonical Ensemble Model %D October 22, 2011 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483 %O application/java

%0 Computer Program %A Engelhardt, Larry %A Chonacky, Norman %D October 22, 2011 %T Boltzmann Distribution from a Microcanonical Ensemble Model %8 October 22, 2011 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11563&DocID=2483

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The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Boltzmann Distribution from a Microcanonical Ensemble Model.