On Wed, Jan 8, 2014 at 1:47 PM, John Clark <johnkcl...@gmail.com> wrote:

> On Tue, Jan 7, 2014 at 1:24 PM, Jesse Mazer <laserma...@gmail.com> wrote:
> > you could have laws where a large number of initial states can all lead
>> to the same final state (many cellular automata work this way, specifically
>> all the ones whose rules are not "reversible"--for example, in the "Game of
>> Life"
> Yes that's what irreversible means, there is more than one way to get into
> a given state.
>  > there are many initial states you can choose that will lead all the
>> black squares to eventually disappear and leave you with all white
>> squares).
> Sometimes the Game of Life ends up oscillating between 2 states, but the
> only time it enters a final state is when all the cells have died.
> Sometimes you might end up with a oscillation between the initial state and
> some other state  but all those examples are trivial and very small (such
> as 3 cells in a straight line). Sometimes the Life pattern just keeps on
> growing forever, and sometimes the Life pattern can emulate a Turing
> Machine. The laws of physics, that is to say the rules of the cellular
> automation, are identical in all these examples, but the initial conditions
> are different.
> If the laws of physics actually make a change in something (and they are
> pretty lame laws if they don't) and if the initial conditions of the
> universe were very low entropy, and if there are more ways to be
> disorganized than organized (and there are) then any change those laws of
> physics make will almost certainly lead to a increase in entropy.
> John K Clark

 OK then, do you agree with the point I was making that deriving the second
law requires conservation of phase space volume (which can be guaranteed by
choosing reversible laws, I think)? If your laws allow for the possibility
that an ensemble of initial microstates occupying a large volume of phase
space can converge on a smaller set of final microstates occupying a
smaller volume, then one can choose one's macrostates in such a way that
high-entropy initial macrostates are more likely to lead to low-entropy
final macrostates--do you disagree? For example, in Life one could define
macrostates in terms of the ratio of white to black cells, and quite a lot
of initial microstates that are in the macrostate of a 50:50 ratio of black
and white (where the number of possible combinations is huge) end up in a
later macrostate where the cells are wholly or almost wholly white (with a
much smaller number of possible microstates, and thus a lower entropy).


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