10.2. Purely mechanical machines[[Student version, January 17, 2003]] 363
fxG-ratchet: S-ratchet:fLLa b
Figure 10.10:(Schematics.) (a)The “G-ratchet.” A rod (horizontal cylinder) makes a supposedly one-way trip to
the right through a hole in a “membrane” (shaded wall), driven by random thermal fluctuations. It’s prevented from
moving to the left by sliding bolts, similar to those in a door latch. The bolts can move down to allow rightward
motion, then pop up as soon as they clear the wall. A possible external “load” is depicted as an applied forcef
directed to the left. The text explains why this device doesnotwork. (b)The “S-ratchet.” Here the bolts are tied
down on the “cell interior” (left side), then released as they emerge on the right.
Sullivan: Couldn’t you wrap your shaft into a circle? Then your machine would go around forever,
constantly doing work against a load.
Gilbert: Just what are you trying to tell me?
Yes, Sullivan is just about to point out that Gilbert’s device would continuously extract me-
chanical work from the surrounding thermal motion, if it worked the way Gilbert supposes. Such
amachine would spontaneously reduce the world’s entropy and so violate the Second Law.^5 You
can’t convert thermal energy directly to mechanical energy without using up something else—think
about the discussion of the osmotic motor in Section 1.2.2.
Sullivan continues: Ithink I see the flaw in your argument. It’s not really so clear that your
device takes only rightward steps. It cannot move at all unless the energyneeded to retract a bolt
is comparable tokBT.But if that’s the case, then the bolts willspontaneouslyretract from time
to time—they are thermally jiggling along with everything else! If a leftward thermal kick comes
along at just such a moment, then the rod will take a step to the left after all.
Gilbert: Isn’t that an extremely unlikely coincidence?
Sullivan: Not really. The applied force will make the rod spend most of its time pinned at one
of the locationsx=0,L, 2 L,.. .,atwhich a bolt is actually touching the wall. Suppose that now
athermal fluctuation momentarily retracts the obstructing bolt. If the rod then moves slightly to
the right, the applied force will just pull it right back to where it was. But if the rod moves slightly
to the left, the bolt will slip under the wall andfwill pull the rod a full step to the left. That is,
an applied force converts the random thermal motion of the rod to one-way,leftward, stepping. If
f=0,there will be no net motion at all, either to the right or left.
Sullivan continues: But I still like your idea. Let me propose a modification, the“S-ratchet”shown
in Figure 10.10b. Here a latch keeps each bolt down as long as it’s to the left of the wall; something
releases the latch whenever a bolt moves to the right side.
Gilbert: Idon’t see how that helps at all. The bolts still never push the rod to the right.
Sullivan: Oh, but they do: They push on the wall whenever the rod tries to take a step to the left,
and the wall pushes back. That is, they rectify its Brownian motion by bouncing off the wall.
Gilbert: But that’s how my G-ratchet was supposed to work!
(^5) Unfortunately it’s already too late for Gilbert’s financial backers, who didn’t study thermodynamics.