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.
- The graph below the gas volume displays the (velocity-) entropy;
the graph is continually rescaled.
++ go faster
- The initialisation of the particle collision tables
is a fairly big task and can take some time.
- The calculations are all done in integers so
there are no rounding errors.
- NB. Needs Java 2 (ish), on!
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"].
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.
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.