MAXWELL'S DEMON
by
Robert Nemiroff
Michigan Tech
Physics X: About This Course
• Officially "Extraordinary Concepts in Physics"
• Being taught for credit at Michigan Tech
o Light on math, heavy on concepts
o Anyone anywhere is welcome
• No textbook required
o Wikipedia, web links, and lectures only
o Find all the lectures with Google at:
 "Starship Asterisk" then "Physics X"
o
http://bb.nightskylive.net/asterisk/viewforum.php?f=39
ENTROPY
What is entropy?
1.
2.
3.
4.
The number of configurations an item can have.
The amount of disorder an item has.
The temperature an item has.
The new compact car by Chevrolet (tm).
ENTROPY
2. The amount of disorder an item has.
For some items, increasing the temperature increases the
entropy. But not always. In general, temperature can vary
across an item, but the item has but one entropy.
ENTROPY
Can the amount of disorder in an isolated item ever decrease
over long periods of time?
1. No, that would be against the 2nd Law of Thermodynamics.
2. Yes, sometimes order increases, sometimes it decreases.
3. Are you saying that if I wait long enough, my room might
clean itself?
ENTROPY
1. No, that would be against the 2nd Law of Thermodynamics.
Entropy is actually a statistical thing. An isolated system can
only become more random (on the average, over time) which
increases entropy.
Bouncing ball example?
MAXWELL'S DEMON
Which of these boxes has the lower entropy?
1. The box on the left.
2. The box on the right.
3. The two boxes in the center.
MAXWELL'S DEMON
2. The box on the right.
The box on the right has more order than the box on the
left. There are fewer ways to arrange the hot and cold particles
to get the box on the right than the box on the left.
MAXWELL'S DEMON
A demon appears that can let particles pass between the two
compartments in the box. What is the minimum amount of
energy this demon must expend to open the door between the
two box compartments
1.
2.
3.
4.
Zero.
The kinetic energy of one of the cold particles.
The kinetic energy of one of the hot particles.
About 1.5 zorkels.
MAXWELL'S DEMON
1. Zero.
The energy could be much less than any other energy in the
problem -- effectively zero. A hair-triggered, smoothly-sliding,
well-oiled door with a spring to bounce it back into a closed
position could be fashioned, for example.
MAXWELL'S DEMON
The demon now chooses to let only fast particles from the left
pass to the right, and to let only slow particles from the right
pass to the left. The demon does this only by opening and
closing his small door at just the right times. Is the demon able
to get all the slow particles on the left and the fast particles on
the right?
1. Yes, good for him.
2. No, that would decrease entropy.
3. I said "maybe" and that's final.
MAXWELL'S DEMON
1. Yes, good for him.
It is clear that the demon can decrease the entropy of the system. And
(s)he can do it using a door that requires almost no energy to open and
close. Does this violate the second law of thermodynamics?
1. Yes, which is good because I never liked that law anyway.
2. No, because somehow, the demon is using energy.
3. I'm not sure, but don't tell the demon, we need the energy.
MAXWELL'S DEMON
2. No, because somehow, the demon is using energy.
It is clear that the second law will hold. No one has ever been able to
build such a demon in practice. Somehow, the entropy of the demon
must be increasing.
MAXWELL'S DEMON
What does the demon do that increases his entropy?
1.
2.
3.
4.
5.
Slides the door open and closed between compartments.
Measures the speeds of the particles.
Thinks about when to open the door between compartments.
Notes the speeds of all of the particles.
Erases the speeds of old particles.
MAXWELL'S DEMON
You probably got this wrong so please choose again.
We'll wait.
MAXWELL'S DEMON
5. Erases the speeds of old particles.
What? Can't he just use a really large USB drive? No. After
some time, any drive will fill up. At that point, the only way to
tell which particles should be let through will involve recording
information that is stored over old information. So information
must be erased. And erasing, oddly enough, seems to be the
key.
MAXWELL'S DEMON: HISTORY
•
•
•
•
•
•
Created by James Clerk Maxwell in the 1860s and 1870s.
First appeared in a letter to a friend in 1867.
Published in his book "Theory of Heat" in 1871.
Term "demon" coined by Lord Kelvin in 1874.
o "demon" really meant mediating, not devilish.
Continually under debate by famous physicists.
Still debated today.
LANDAUER'S PRINCIPLE
Erasing information creates entropy.
Erasing information is an irreversible process. Think of it like
erasing chalk on a blackboard -- the chalk need not GO
anywhere -- but it becomes more randomized.
To erase something on a physical device, it turns out, must
increase the entropy. Erasing information on even the smallest
device will result in an entropy increase.
The smallest bit of information erasure seems to be kT ln 2
MAXWELL'S DEMON
Recent analyses include the energy the demon must use, and
hence the entropy the demon must generate. The analyses
STILL has controversial aspects, though.
So that uneasy feeling you have about this -- some physicists
still have that feeling as well.