The experiment is simple.
Think a chamber in which a partition wall is set to make equal two rooms.
In the left room a gas is enclosed, while the right room is empty, that is, vacuum.
Take the partition wall quickly, and watch what happens.
The gas molecules will diffuse to occupy both rooms by equal numbers.
Finally the gas will fill the entire chamber and reaches thermodynacmical equilibrium.
Plot the entropy of the gas against time abscissa.
Please choose your answer from the followings.
Answer 1: Considering based on the principle of increase of entropy, such an entropy curve must show one-way increase, it never goes down again. The Poincare cycle is too long to be actually meaningful. The increase of entropy is absolutely irreversible.
Answer 2: The concept of Poincare cycle is valid. The entropy curve must show semi-periodical behavior. That is, the entropy increases first then decrease and increases again, and repeats this cycle forev er. Even if the time length of the Poincare cycle is extraordinarily long, what can happen will happen. This is your favorite Murphy's law ( Ah,ha,ha.ha.)
P.S. By using the current computer and assuming a gas composed from only several handreds particles, I think we can do the simulation and can draw the entropy curve against time abscissa, and investigate it.
A man who has recently begun to read a book "The Quantum Story" written by Jim Baggot published from Oxford University Press. This book is really a precious treasure for me.
February 13, 2013