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WOLFRAM|DEMONSTRATIONS PROJECT

Molecules Distributed between Two Compartments

left
25
right
5
steps
60
seed
possible configurations=119759850
A box has two compartments connected by a hole. There are
n
l
molecules in the left compartment and
n
r
in the right.
To update the original values of
n
l
and
n
r
, generate a pseudorandom number
r
between 0 and 1; if
r<
n
l
/(
n
l
+
n
r
)
, a molecule is added to the left and one is taken away from the right. If
r>
n
l
/(
n
l
+
n
r
)
, 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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