I don't have any goal in mind here with any of my posts. I'm just exploring.
Exploring is an excellent thing to do ... but while exploring, it is
good to look around for practical applications.
It turns out that there are real-world applications that depend on
understanding what does -- and does not -- contribute to the dissipation.
As a warm-up exercise, consider the task of lowering an anvil from the
2nd floor to ground level. The anvil starts out with energy mhg. If
you just throw the anvil out the window, all the energy is dissipated
when it smashes into the ground. Similarly, if you let the anvil slide
slowly down a ramp, all the energy is dissipated in sliding friction.
On the other hand, if you let the anvil ride down an escalator, it
does work against the escalator motor, and in principle you could
capture that energy and sell it, or do something else useful with it.
This has application to the physics of computing. On the chip, logical
ones and zeros are represented as voltages stored on nodes that are
basically capacitors. Logic gates are basically switches that pull the
voltage down to ground or up to Vdd. Suppose the node starts at Vdd
and you want to pull it down to ground. This dissipates 1/2 C V^2. The
energy is dissipated as heat in the internal resistance of the switch.
On the other hand, if you are clever, rather than closing a switch between
the node and ground, you can close a switch between the node and a /ramp/
that gradually ramps down from Vdd to zero. The current (I) depends on
how fast the ramp is ramping down. The total charge goes like the integral
of I dt, while the total energy dissipated goes like the integral of I^2 dt.
The instantaneous current is less ... and the instantaneous power is
/disproportionately/ less. Most of the 1/2 C V^2 energy gets pumped back
into the clock-driver circuit. It's analogous to letting the anvil ride
down the escalator.
Circuits that work this way have been built. There are patents on the
subject. See e.g. http://www.google.com/patents/US5559463 and the 20
or so other patents that refer to it.
To a first approximation, the scaling law is simple: The energy per unit
computation scales like the RC time of the node, divided by the ramp-time.
This means that if you clock the circuit slowly, you can save a huge amount
of energy.
Actually it's even better than that, because chips already run at with a
clock rate many times slower than the 1/RC rate. That's because on a
chip with millions of transistors, there's always a weak one somewhere,
with an RC time that is much longer than it nominally should be. So if
you want to get the right answer, you need to run much slower than the
nominal 1/RC rate. However, to achieve low power, you don't need to lower
the clock rate /again/. Having one transistor out of a million that is
more dissipative than it should be is harmless.
This is an interesting story, because for many decades people got this
wrong. A bunch of reeeeally smart people got it wrong. Every textbook
on integrated circuit design said that chips would always dissipate 1/2
C V^2 per logic operation, and there was nothing you could do about it
(other than lowering the capacitance and/or lowering the voltage). It
was known that "reversible computing" was possible, but everybody believed
it couldn't be done using ordinary CMOS logic gates. We now know better.
It is most definitely possible to dissipate a lot less than 1/2 C V^2 per
operation using ordinary CMOS technology.
A lot of non-scientists think that science consists of expeditions à la
Lewis and Clark, going far into the wilderness, far from the beaten path,
discovering things that nobody has ever imagined before. Sometimes it
works that way, but sometimes not. Sometimes it consists of looking at
something that is right in the middle of the beaten path and saying Hey,
wait a minnit! Are you sure about that? How do you know? How do you
reconcile that with these other six things that we know?????
Bjarne Stroustrup calls this "playing in traffic".