CSW's Reversible Gas

The physics of this two-dimensional gas (Java applet below) are reversible. Time can be run forwards and backwards. Energy is perfectly conserved. A small graph of the recent entropy is also plotted; this is continually rescaled to use all of its y-axis.

Chris Wallace showed that this artificial gas obeys many of the properties of real gases -- see the 'Feathers on the Arrow of Time' chapter in ["the MML book"].

Entropy

The plotted entropy is the "velocity" entropy with both the x & y velocity components of the particles "folded" together onto the positive axis.

It can be seen that from a randomly selected state, the entropy is equally likely to be higher or lower in the next (or previous) state.

However, if the gas is observed to be in a low entropy (ordered) state at time t, it will almost certainly be in a higher entropy state at time t+1, and the time-reversibility implies that it was almost certainly in a higher entropy state at time t-1.

Determinism: 1-1 State Transitions

The physics of the gas are deterministic. Therefore the states will cycle  - over  a  v e r y  l o n g  period, N. From this point of view the entropy of every state is the same, log(N).

© C.S.Wallace & L.Allison.