Molecules Distributed between Two Compartments

A box has two compartments connected by a hole. There are molecules in the left compartment and in the right.
To update the original values of and , generate a pseudorandom number between 0 and 1; if , a molecule is added to the left and one is taken away from the right. If , a molecule is added to the right and one is taken away from the left.
With a large number of molecules on one side and a small number on the other side, the system tends to equilibrium after some steps, with small fluctuations afterward. Clearly the entropy of the system increases, evolving to a more disordered state and giving an "arrow of time", making it possible to distinguish the past from the future. But experimenting with a small number of particles is not enough to distinguish past from future. This is because a system with a large number of molecules has a huge number of microstates, and a small system has just a few.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The entropy is .
The number of possible configurations for a particular number of particles in the left compartment is equal to the binomial coefficient .
This experiment is quoted by Stephen Wolfram as an early inspiration that led him to write A New Kind of Science.
F. Reif, Statistical Physics, Berkeley Physics Course, Vol. 5, New York: McGraw-Hill, 1967.
R. M. Eisberg and L. S. Lerner, Physics: Foundations and Applications, Vol.
2, New York: McGraw-Hill, 1981.
See Statistical Mechanics and Microstate on Wikipedia for more information.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+