Stan,
The relationship between QM and dissipation, of prime importance to
biology, is quite intriguing because of the unbridgeable gap between the
two. One is discontinuous when measurement intervenes, while the other is
continuous. A nice thing about the probabilistic scheme is that it makes the
whole edifice continuous with respect to the probability measure. Once the
discontinuous aspects under the continuous outerwear are focused upon
instead,
the theoretical enterprises upon continuous spaces would not help us much.
The issue would become most acute when one pays attention to the formation
and transformation of each quantum as a discrete and discontinuous unit,
though the boundary conditions of our choice may reflect the underlying
discontinuous nature if we are lucky enough.
At this point enters thermodynamics. The first law is on the likelihood
of energy transformation, while the second law is about the possibility of a
heat engine processing energy transformation. Heat engine is a discrete,
organized unit processing dissipation in a continuous manner. If one takes a
quantum as a basic unit of material dynamics, the 1st and 2nd laws, when put
together, may suggest occurrence of a quantum as a heat engine. (Jamie seems
to have a more encompassing scheme on this.) One checkpoint of this scenario
is to see whether what looks like a heat engine as a discrete unit, most
relevant on the verge of the origins of life, could emerge in the
presence of some form of gradients. If a heat engine of
emergent character happens to be faster in harnessing the gradients compared
to other contenders, it will win the race. The winner takes all. The
distinction between the winner and the loser remains discrete and robust
while the race takes place on the continuous track.
A perspective from a little bit closer to the lab bench?
Koichiro
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Received on Mon Jun 26 01:19:04 2006
