On Wed, Jan 8, 2014 at 1:47 PM, John Clark <[email protected]> wrote:
> > On Tue, Jan 7, 2014 at 1:24 PM, Jesse Mazer <[email protected]> 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). Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
