Molecules Distributed between Two Compartments

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A box has two compartments connected by a hole. There are molecules in the left compartment and in the right.

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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.

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Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA


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Details

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.

References:

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.



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