From: Anders Sandberg (asa@nada.kth.se)
Date: Fri Jul 19 2002 - 01:52:52 MDT
On Fri, Jul 19, 2002 at 12:55:35AM -0400, Spudboy100@aol.com wrote:
> I wonder what "consumed entropy" does to the universe? Lots of little actions
> on the micro-scale may have large impacts.
On average, they have no impact beside the noise: that entropy
increases is just a consequence of that the universe is on
average moving from a less likely state to a more likely state.
If you look at every transition you will see a lot of local
violations of the second law, but on larger scales they become
more and more unlikely, until you end up with a probability
infinitsimally smaller than 1 of entropy increasing.
As an example, imagine a gas with rho molecules/m^3 and a box
of length L. There will be around rho L^3 molecules in it
randomly bouncing around. The probability that all will be on
the left side (I would like to say more than 51%, but the
calculations get messy; they are left as an exercise for the
student :-) is P=2^-(rho L^3). So if we assume rho to be
10^24/m^3, the probability for L=1 m is 2^-10^24, or
essentially zero. If L is one micrometer then the probability
is 2^-10^6, still extremely small. If you go down to a ten
nanometers, then the probability is suddenly around 2^-10 or
one in 1024. Below this the probability rapidly increases
(although complications occur because there is also a large
chance there will be no molecules at all in our box). So we
ought to see brief thermodynamic fluctuations on this scale
where entropy is not conserved, even if it is on the larger
scale.
These fluctuations can be exploited by nanomachines, but only
locally. See Tom Schneider's work at www.lecb.ncifcrf.gov/~toms
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
This archive was generated by hypermail 2.1.5 : Sat Nov 02 2002 - 09:15:34 MST