Demons, Engines and the Second Law
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Demons, Engines
and the Second Law
Since 1871 physicists have been trying to resolve the conundrum
of Maxwell's demon: a creature that seems to violate the second law
of thermodynamics. An answer comes from the theory of computing
by Charles H. Bennett
O
ne manifestation of the sec these effects would be to abolish the simple inanimate device, for instance
ond law of thermodynamics is need for energy sources such as oil, a miniature spring-loaded trapdoor.
that such devices as refrigera uranium and sunlight. Machines of Like Maxwell's original demon, the
tors, which create inequalities of tem all kinds could be operated without "pressure demon" could be a source
perature, require energy in order to batteries, fuel tanks or power cords. of limitless power for machines. For
operate. Conversely, an existing in For example, the demon would en example, pneumatic drills of the kind
equality of temperature can be ex able one to run a steam engine con used to cut holes in streets generally
ploited to do useful work-for exam tinuously without fuel, by keeping run on compressed air from a tank
ple by a steam engine, which exploits the engine's boiler perpetually hot kept full by a gasoline-powered com
the temperature difference between and its condenser perpetually cold. pressor. A one-way valve for air mol
its hot boiler and its cold condenser. To protect the second law, physi ecules could substitute for the com
Yet in 1871 the Scottish physicist cists have proposed various reasons pressor, effortlessly collecting air
James Clerk Maxwell suggested, in the demon cannot function as Max from the surroundings into the high
his Theory of Heat, that a creature well described. Surprisingly, nearly pressure tank.
small enough to see and handle indi all these proposals have been flawed. One might think such an arrange
vidual molecules might be exempt Often flaws arose because workers ment would violate the law of conser
from this law. It might be able to cre had been misled by advances in oth vation of energy (otherwise known
ate and sustain differences in temper er fields of physics; many of them as the first law of thermodynamics),
ature without doing any work: thought (incorrectly, as it turns out) but it would not. The energy for cut
". . .if we conceive a being whose that various limitations imposed by ting concrete could be taken from
faculties are so sharpened that he quantum theory invalidated Max heat in the air collected by the one
can follow every molecule in its well's demon. way valve; the air's temperature
course, such a being, whose attri The correct answer-the real rea would drop as it passed through the
butes are still as essentially finite as son Maxwell's demon cannot violate machinery. There is nothing in the
our own, would be able to do what is the second law-has been uncovered first law to prevent an engine from
at present impossible to us. For we only recently. It is the unexpected supplying all its energy needs from
have seen that the molecules in a result of a very different line of the ambient heat of its environment,
vessel full of air at uniform tempera research: research on the energy re or even from the waste heat of its
ture are moving with velocities by no quirements of computers. own friction and exhaust. It is the sec
means uniform. . . . Now let us sup ond law that prohibits such engines.
S sions of the demon have been pro
pose that such a vessel is divided ince Maxwell's day numerous ver To analyze the demon's actions
into two portions, A and B, by a divi closely, then, one must understand
sion in which there is a small hole, posed. One of the simplest creates some of the subtleties of the second
and that a being, who can see the in a pressure difference (rather than a law. The second law was original
dividual molecules, opens and closes temperature difference) by allowing ly expressed as a restriction on the
this hole, so as to allow only the all molecules, fast or slow, to pass possible transformations of heat and
swifter molecules to pass from A to B, from B to A but preventing them from work, but it is now seen as being fun
and only the slower ones to pass passing from A to B. Eventually most damentally a statement about the in
from B to A. He will thus, without of the molecules will be concentrated crease of disorder in the universe.
expenditure of work, raise the tem in A and a partial vacuum will be cre According to the second law, the en
perature of B and lower that of A, in ated in B. This demon is if anything tropy, or disorder, of the universe as
contradiction to the second law of more plausible than Maxwell's origi a whole cannot be made to decrease.
thermodynamics." nal demon, since it would not need This means that only two kinds of
The "being" soon came to be called to be able to see or think. It is not im events are possible: events during
Maxwell's demon, because of its far mediately evident why such a de which the entropy of the universe
reaching subversive effects on the mon-a one-way valve for mole increases and events during which
natural order of things. Chief among cules-could not be realized as some it remains constant. The former are
108 © 1987 SCIENTIFIC AMERICAN, INC
UNIFORM GLOW in a hot furnace (top) demonstrates one conse darker than its surroundings, it would absorb energy at the ex
quence of the second law of thermodynamics: it is impossible to pense of its neighbors. As a result it would become hotter and its
distinguish objects in a vessel at uniform temperature without neighbors would become cooler. According to the second law,
an external light source hotter than the vessel's ambient temper however, objects that are initially at the same temperature can
ature. In a vessel at uniform temperature objects glow in such a not spontaneously come to have different temperatures. (In this
way that exactly the same intensity and color of light come from photograph some contrast is visible because the temperature in
the surface of every object (even objects that have different re side the furnace is not exactly uniform.) By an external light
fiectances and colors). The reason is that if any object appeared source, intrinsic differences in reflectance are visible (bottom).
© 1987 SCIENTIFIC AMERICAN, INC 1 09
ROOM A ROOM B
•
Can this concept be quantified? In
other words, can one say hciw much
the disorder of the gas has increased
after it has spread out to fill both
...
• ... . chambers? Consider a single mole
cule in the gas. A molecule that can
roam throughout both chambers has
....
. • .... twice as many possible positions as a
molecule confined to a single cham
,' .
ber: there are twice as many ways for
a molecule to occupy the two-cham
• ber apparatus. If there are two mole
cules in the two-chamber apparatus,
each molecule has twice as many
possible positions as it would have in
••
a single chamber, and so the system
as a whole has 2 X 2, or four, times
•• as many possible configurations. If
there are three molecules, the sys
tem has 2 X 2 X 2, or eight, times as
many possible configurations.
MAXWELL'S DEMON, described in 1871 by James Clerk Maxwell, seems able to violate In general, if there are n molecules
the second law of thermodynamics. The demon controls 'a sliding door that blocks a in the gas, the gas can fill two cham
hole in a wall between rooms containing gas at equal temperatures and pressures. It ob· bers in 2" times more ways than it
serves molecules approaching the hole and opens and closes the door to allow fast
can fill a single chamber. The gas in
moving molecules to pass from room A to room B but not vice versa. Slow-moving mole
the two-chamber apparatus is said to
cules, conversely, are allowed to pass only from B to A. As the demon sorts, B heats up
have 2" times as many "accessible
and A cools. According to the second law, a certain amount of work is required to create
a temperature difference, but the work of sliding a door can be made negligibly small.
states" as the gas in a single cham
ber. In the same way, the number of
accessible states in most systems de
pends exponentially on the number
known as irreversible processes be cules is due to chance rather than of molecules.
cause to undo them would violate the to repulsion, there is a chance that The entropy of a system is there
second law; the latter are called re all the molecules might return si fore defined as the logarithm of the
versible processes. One can decrease multaneously to the chamber from number of accessible states. In the
the entropy of a given system by do which they came. If there are n mol example of the two-chamber gas ap
ing work on it, but in doing the work ecules, however, the probability of paratus, a 2"-fold increase in the num
one would increase the entropy of all of them returning to their original ber of accessible states is an increase
another system (or that of the first chamber is the same as the probabili in entropy of n bits, or binary units.
system's environment) by an equal ty of tossing n coins and having them (The base of the logarithm-and
or greater amount. all come up "heads": 1/2". Thus for hence the size of a unit of entropy-is
A classic irreversible process, and any sizable number of molecules arbitrary; it is conventional to choose
one that helps in defining the con (and there are about 300,000,000,- base 2 and binary units.) The loga
cept of entropy a little more precise 000,000,000,000,000 molecules in a rithmic scale has the advantage of
ly, is called free expansion. Suppose gram of hydrogen) the free expan making the entropy of a sample
a chamber filled with gas is separated sion is an effectively irreversible of matter, like its energy or mass,
by a partition from a vacuum cham process: a process whose spontane roughly proportional to the number
ber of the same size. If a small hole is ous undoing, although possible, is so of molecules in the sample. One can
made in the partition, gas will escape unlikely that one can say with confi draw an analogy to a computer mem
(that is, it will expand freely) into the dence it will never be observed. ory: an n-bit memory, other things
formerly empty chamber until both being equal, has size, weight and cost
T which the gas has spread into
chambers are filled equally. he disordered state-the state in that are roughly proportional to n, al
The reason the molecules spread though the number of distinct states
out to fill both chambers is mathe both chambers rather than resid possible in the memory is 2".
matical rather than physical, if such a ing compactly in a single chamber
T ond law did not mention random
distinction can be made. The num is more probable than the ordered he earliest statements of the sec
bers of molecules on the two sides of state. That is, there are more config
the partition tend to equalize not be urations of molecules in which the ness or disorder; they concerned
cause the molecules repel one anoth molecules occupy both chambers, heat, work and temperature. How
er and move as far apart as possible, just as, when 100 coins are tossed, can these concepts be related to our
but rather because their many colli there are more ways to achieve a to quantitative definition of entropy?
sions with the walls of the container tal of 50 heads and 50 tails than there The molecules in any sample of
and with one another tend to distrib are to achieve 100 heads and no tails. matter are always in motio)1. The
ute them randomly throughout the In saying that the entropy of the uni speed and direction of each molecule
available space, until about half of verse tends to increase, the second are random, but the average speed of
them are on one side of the partition law is simply noting that the uni the molecules is proportional to the
and about half are on the other side. verse tends to fall into more probable square root of the sample's temper
Since the spreading of the mole- states as time passes. ature (as measured from absolute
110 © 1987 SCIENTIFIC AMERICAN, INC
zero). As the temperature of a sample law (by doing what the demon can to the average kinetic energy of the
is raised (and the average speed in do) simply because they lack the de gas molecules. In 1912 Marian Smolu
creases) the velocities of individual mon's ability to see and handle indi chowski pointed out that because the
molecules come to be distributed vidual molecules. This is not a com door is repeatedly being struck by
over a greater range than they are pletely satisfying exorcism of the molecules, it will eve.ntually acquire
when the average speed is low. demon, because it leaves open the its own kinetic energy of random mo
When the average speed is high, question of whether a being able to tion (that is, heat energy). The door's
then, every molecule in the sam see and handle individual molecules, energy of random motion will be
ple has a greater range of velocities if such a being did exist, could violate about the same as that of the mole
available to it, just as a molecule in the second law. cules striking it, and so the door will
a two-chamber gas apparatus has a One way to uncover the reasons jiggle on its hinges and swing open
greater range of positions available Maxwell's demon cannot work is to and shut (remember that the door
to it than a molecule in a single-cham analyze and refute various simple, is very small), alternately bouncing
ber apparatus has. There are thus inanimate devices that might func against its jamb and swinging open
more accessible states at high tem tion as demons, such as the mini against the force of the spring.
peratures than there are at low tem ature spring-loaded trapdoor men When the door is open, it obviously
peratures. The motion is more disor tioned above, which acts as a one cannot function as a one-way valve,
dered at high temperatures, because way valve for molecules. since molecules can pass freely in
it is harder to predict what the veloci Imagine that the door opens to the both directions. One might still hope
ty of any molecule will be. left. If the demon works as it is sup that the door would act as an ineffi
Disorder of molecular motion and posed to, then every time a molecule cient demon, trapping at least a small
disorder of molecular positions must from the room on the right strikes the excess of gas on the left, but it cannot
both be counted in determining the door, the door swings open and the do even that. Any tendency the door
entropy of a system. The entropy of a molecule passes into the room on has to act as a one-way valve, open
gas can be increased either by allow the left. When a molecule from the ing to let a molecule go from the right
ing the gas to occupy a greater vol left strikes the door, however, the to the left, is exactly counteracted
ume or by increasing its temperature door slams shut, trapping the mole by its tendency to do the reverse: to
so that its molecular motion becomes cule. Eventually all the molecules are slam shut against a molecule that has
more disorderly. trapped on the left, and the demon wandered in front of it, actively push
Any flow of heat therefore carries has compressed the gas (reducing its ing the molecule from the room on
entropy with it. To be precise, it turns entropy) without doing any work. the left to the one on the right (aided
out that a heat flow carries an How is the trapdoor demon flawed? by the force of the spring).
amount of entropy proportional to First of all, the spring holding the The two processes-a molecule
the quantity of heat flowing divided door shut must be rather weak. The pushing its way past the door from
by the temperature at which the flow work of opening the door against the right to left, and the door pushing a
takes place. Hence a flow from a hot spring's force must be comparable molecule from left to right-are me-
ROOM A
body to a cold body raises the entro
py of the cold body more than it low
ers the entropy of the hot one: the
same amount of heat leaves the hot
body as enters the cold body, but in
figuring the entropy decrease of the
hot body one divides by a high tem ••
perature, whereas in figuring the en
tropy increase of the cold body one
divides by a low temperature. A heat
•
flow from a hot to a cold body thus
raises the entropy of the universe.
O tropy gives us a better under
ur more precise definition of en
standing of why Maxwell's demon
seems to violate the second law. By
its sorting action the demon is caus
ing heat to flow from room A to room
B, even after room B has become
warmer than room A. The demon is
therefore lowering the entropy of
room A by a greater amount than it is
TRAPDOOR "DEMON" is a form of Maxwell's demon designed to operate automatical
raising the entropy of room B. The de
ly and to create an inequality of pressure, not of temperature. A spring-loaded trapdoor
mon therefore decreases the entropy
blocks a hole between two rooms initially containing gas at equal temperatures and
of the universe as a whole-a thermo
pressures. The door swings open in only one direction in order to admit molecules
dynamic impossibility.
from room B into room A but not vice versa. Eventually, one might think, molecules will
In his description of the demon accumulate in A at the expense of B, creating an inequality of pressure. Actually the in
Maxwell made it clear he believed in equality does not build up. The trapdoor, heated by collisions with molecules, jiggles
the validity of the second law. He open and closed randomly because of thermal energy. When it is open, it is not a one
suggested that perhaps human be way valve, and as it closes it may push a molecule from A into B. The latter process takes
ings are unable to violate the second place as often as its inverse, in which a molecule from B pushes past the door into A.
© 1987 SCIENTIFIC AMERICAN, INC 111
a b
••
• .. .
•. . . .
0 °
.
•• . .
. . ..
..
.
• •
.... • •
•
• .
••
'
•.. .. ... • .
'
... '. •
•
•...
� .,. .'
....
. . '
.. •• '.
• .
••
"
• . "
•
•
FREE EXPANSION of a gas is a thermodynamically irreversible chamber apparatus (a). The barrier between the chambers is
process: one in which the entropy, or disorder, of the universe pierced, and molecules leak from one chamber into the other un
increases. A gas is initially confined in one chamber of a two- til approximately the same number of molecules are in both (b)_
chanical reverses of each other: a question in a paper published in possible states: a blank state to signi
motion picture of one, shown back 1929, "On the Decrease of Entropy in fy that no measurement has been
ward, would look like the other. In an a Thermodynamic System by the In made, an L to signify that the mole
environment at a constant temper tervention of Intelligent Beings." Al cule has been observed in the left
ature and pressure both processes though the title seems to imply an in half of the apparatus, and an R to sig
would take place equally often, and telligent demon could violate the sec nify that the molecule has been ob
the ability of the trapdoor to act as ond law, the body of the article is served in the right half. When the
a one-way valve would be exactly devoted to refuting this notion and to measurement is made, the memory
zero. It cannot work as a demon. arguing that no being, intelligent or switches from the blank state to one
In environments where the pres not, can do so. Szilard thought the ob of the other two.
sure is not equal on both sides of servation, or measurement, the de The third step, which might be
the door, of course, such devices do mon must make (for example, to see called a compression stroke, de
function. Large-scale versions, built which side a molecule is coming pends on the knowledge gained dur
with macroscopic doors and springs, from) cannot be done without also ing the preceding step. The piston on
can be seen on ventilator fans de doing enough work to cause an in the side that does not contain the
signed to blow stale air out of restau crease in entropy sufficient to pre molecl,lle is pushed in until it touches
rants without admitting gusts of out vent a violation of the second law. the partition. Unlike the compression
side air when the fan is off. Micro Szilard considered a demon that stroke of an internal-combustion en
scopic versions would function in differed in several ways from Max gine, this compression stroke re
much the same way, allowing mole well's; his demon has since come quires no work, because the piston
cules to pass if there were excess to be called Szilard's engine. (The is "compressing" empty space; the
pressure on one side but shutting off engine I shall describe here differs molecule, which is trapped on the
the flow if there were excess pres slightly from Szilard's original one.) other side of the partition, cannot re
sure on the other. The devices would The engine's main component is a sist the piston's movement.
not violate the second law, because cylinder in which there is a single Then, in the fourth step, the parti
they could only allow pressures to molecule in random thermal motion. tion is removed, allowing the mole
equalize; they could never form re Each end of the cylinder is blocked cule to collide with the piston that
gions of excess pressure. by a piston, and a thin, movable par has just been advanced. The mole
tition can be inserted in the middle of cule's collisions exert a pressure on
E demon cannot work, perhaps an
ven though a simple mechanical the cylinder to trap the molecule in the face of the piston.
one half of the cylinder or the other In the fifth step, which might be
intelligent one can. Indeed, some [see illustration on opposite page]. The called the power stroke, the pressure
time after Maxwell had described the engine is also equipped with devices of the molecule drives the piston
demon, many investigators came to for finding which half of the appara backward to its original position, do
believe intelligence was the critical tus the molecule is in and a memory ing work on it. The energy the mole
property that enabled the demon to for recording that information. cule gives to the piston is replaced by
operate. For example, in a 1914 paper The engine's cycle consists of six heat conducted through the cylinder
Smoluchowski wrote: "As far as we steps. In the first step the partition is walls from the environment, and so
know today, there is no automatic inserted, trapping the molecule on the molecule continues moving at
permanently effective perpetual-mo one side or the other. Szilard argued the same average speed. The effect of
tion machine, in spite of the molecu that the work necessary to insert the the power stroke is therefore to con
lar fluctuations, but such a device partition can in principle be made vert heat from the surroundings into
might, perhaps, function regularly if negligibly small. mechanical work done on the piston.
it were appropriately operated by in In the next step the engine deter In the sixth step the engine erases
telligent beings." mines which half of the apparatus the its memory, returning it to the blank
The physicist Leo Szilard attempt molecule has been trapped in. The state. The engine now has exactly
ed a quantitative analysis of this engine's memory device has three the same configuration it had at the
112 © 1987 SCIENTIFIC AMERICAN, INC
beginning of the cycle, and the cycle cule to be observed it must scatter at
MEMORY tMOVAB
PARTITILOEN
can be repeated.
verall, the six steps appear to
least one photon of a probe beam,
and that when the photon's energy is 6 i\
-1J� G-
O
dissipated into heat, the dissipation
have converted heat from the must produce an entropy increase at
surroundings into work while return least as great as the entropy decrease
ing the gas and the engine to the Szilard's engine could achieve as the
same state they were in at the start. If result of information gained about
no other change has occurred during the scattering molecule.
the cycle of operation, the entropy of 2
the universe as a whole has been
lowered. In principle the cycle can be W
hy not simply use a probe beam
of photons that have very low
o
repeated as often as the experiment energies? The scheme will not work,
er wants, leading to an arbitrarily because of another, more complicat
large violation of the second law. ed, consequence of the quantum the
Szilard's way out of this predica ory. According to the quantum the
ment was to postulate that the act ory of radiation, any vessel whose
of measurement, in which the mole walls and interior are all at a single
cule's position is determined, brings constant temperature becomes filled
about an increase in entropy suffi with a "gas" of photons: a bath of ra
cient to compensate for the decrease diation. The wavelengths of the pho
in entropy brought about during the tons depend on the temperature of
power stroke. Szilard was somewhat the vessel. Such a photon gas consti
vague about the nature and location tutes the uniform red or orange glow
of the increase in entropy, but in the inside a hot furnace. (At room tem
years after he published his paper a perature the photons are mostly in
number of physicists, notably Leon the infrared part of the spectrum and 4
Brillouin (the author, in 19 56, of the are therefore invisible.)
widely read book Science and Infor
�I'/G-
The photon gas might seem at first
mation Theory) and Denis Gabor (best to be a handy source of light by
known as the inventor of hologra which the demon could observe gas
phy), tried to substantiate the postu molecules (thereby saving itself the
lated irreversibility of measurement. entropy cost of a flashlight). One of
....R �I
... _t
In particular they tried to determine the surprising consequences of the
what the cost should be, in terms of second law, however (a consequence
5
energy and entropy, of observing a discovered by Gustav Robert Kirch
molecule by aiming light at it and ob hoff in 1859), is that it is impossible to �
serving the reflections. see anything in a vessel at ufliform
In their work, Brillouin and Gabor temperature by the light of the ves
drew on a theory that had been de
veloped since Maxwell's time: the
quantum theory of radiation. Accord
ing to the classical wave theory of
light (to which Maxwell made funda
sel's own glow. If one looks into a
kiln in which pots are being fired, for
example, one will see a uniform or
ange glow almost devoid of contrast,
even though the pots in the kiln may
--4.G-
mental contributions), the energy of have very different colors, bright
a light ray can be made arbitrarily nesses and surface textures.
small. According to the quantum the The objects in the hot kiln look as
ory, however, light consists of ener if they are all the same color and
gy packets called photons. The ener brightness, but they are not, as one
HEAT
gy of a photon depends on its wave can verify by shining a bright light
� ���
length, or color, and it is impossible on them from outside the kiln. The
I
to detect less than one photon of reason the objects nearly disappear
by the light of the kiln must therefore 7
light. Brillouin argued that for a mole-
R
SZILARD ENGINE, modeled after a machine described in 1929 by Leo Szilard, seems to
convert heat from its surroundings into work, contrary to the second law. The engine
(1) is a cylinder that is blocked off at both ends by pistons; it is equipped with a movable
partition and devices for observing the cylinder's contents and recording the results of
observations. The cylinder contains a single molecule. At the start of the engine's cycle
-1J� G-
8
. '
(2) the partition is lowered, trapping the molecule in one half of the cylinder. The obser
vational devices determine and record which half contains the molecule (3), and the
piston from the other half is pushed in until it touches the partition (4). Moving the pis
ton requires no work, since it compresses empty space. Then the partition is with
drawn (5) and the molecule strikes the piston, pushing it backward (6). (The one-mole
cule gas "expands" against the piston.) Energy lost by the molecule as it works against
the piston is replaced by heat from the environment. When the piston has returned
to its original position (7), the memory is erased (8) and the cycle can begin again.
© 1987 SCIENTIFIC AMERICAN, INC 113
FRAME
2
LOCKING PIN-
4
5
t MEASUREMENT APPARATUS, designed by the author to fit the
Szilard engine, determines which half of the cylinder the mole
cule is trapped in without doing appreciable work. A slightly
modified Szilard engine sits near the top of the apparatus (1)
within a boat-shaped frame; a second pair of pistons has re
placed part of the cylinder walL Below the frame is a key, whose
position on a locking pin indicates the state of the machine's
memory_ At the start of the measurement the memory is in a
neutral state, and the partition has been lowered so that the mol
ecule is trapped in one side of the apparatus_ To begin the meas
urement (2) the key is moved up so that it disengages from the
locking pin and engages a "keel" at the bottom of the frame_
Then the frame is pressed down (3)_ The piston in the half of the
cylinder containing no molecule is able to descend completely,
but the piston in the other half cannot, because of the pressure
of the molecule_ As a result the frame tilts and the keel pushes
the key to one side_ The key, in its new position, is moved down
to engage the locking pin (4), and the frame is allowed to move
back up (5), undoing any work that was done in compressing the
molecule when the frame was pressed down_ The key's position
indicates which half of the cylinder the molecule is in, but the
work required for the operation can be made negligible_ To re
verse the operation one would do the steps in reverse order_
114 © 1987 SCIENTIFIC AMERICAN, INC
be that dark (that is, nonreflective)
objects glow proportionately more
brightly than light (reflective) ob·
jects, so that the total light intensi·
The Collected Papers
of Albert Einstein
ty leaving any object (reflected and
emitted light combined) is the same.
To see why this strange leveling of
intensity must take place, suppose it Volume I. The Early Years: 1879-1902
did not occur and think about the John Stache/, Editor
consequences for the second law.
Suppose two objects, say a vase and David C Cassidy and Robert Schu/mann, Associate Editors
a pot, are placed close together in a
Princeton University Press "This first instal/ment appears
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ward the pot were greater than that
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ergy would flow from the vase to the
documentation of the history paradigm of academic publishing
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I Princeton University Press
In order to see the objects in a fur·
nace, then, one must shine light in
II 41 WILLIAM STREET. PRINCETON, NJ 08540 • (609) 8%·1344
from an external source, such as a
flashlight that has a filament hotter
than the furnace's temperature. In
NO EXPERIENCE
daily life such light sources-the sun,
for example-make it possible for us
to see objects in vessels that are uni
formly at room temperature.
A letter quality daisy wheel
Brillouin, Gabor and others, armed
with an understanding of the photon
word processor you can ./�
gas, argued that Maxwell's demon use from day one.
cannot observe the molecules it sorts
without some kind of light source. Nothing technical
Therefore, they said, the demon can· to learn or
not violate the second law. Every memorize. "On
time it observes a molecule the de· Screen" prompts
mon must dissipate the energy of at enable you to
least one photon; the energy of that type, store, recall,
photon must be greater than a mini edit and print
mum energy determined by the tem at the touch
perature of the gas in which the de ofakey. And
mon sits. Such arguments, although it's as easy
they are not completely rigorous, to afford
seemed to substantiate Szilard's be· as it is to
lief that acquiring a given amount of use.
information entails producing a cor·
responding amount of entropy.
Brother International Corp.
Piscataway, NJ 08854
T
he next major progress toward
banishing the demon was a side Call toll free l-8OQ·284-HELP
effect of research by Rolf Landauer of
IBM on the thermodynamics of data
processing. Certain data-processing
operations, such as the copying of
data from one device into another,
are analogous to measurements, in
that one device acquires information
about the state of the other. Hence it
© 1987 SCIENTIFIC AMERICAN, INC 115
was generally believed in the 19 50's phrase, such operations are "logical the resetting step rather than to the
that data-processing operations were ly irreversible." measurement step may seem to be a
intrinsically irreversible (in the ther The connection of these ideas to mere bookkeeping formality, since
modynamic sense of the word), just the problem of the measurement, im any complete cycle of Szilard's' en
as Szilard had argued that measure plicit in Landauer's work and in the gine must include both steps, but
ment in general is irreversible. It was reversible models of computation de considerable confusion can be avoid
thought that any kind of data opera veloped during the 1970's by Edward ed if one draws a clear distinction be
tion required the generation and re Fredkin of M.l.T., myself and oth tween the acquisition of new infor
moval of at least one bit's worth of ers, became explicit in 1982, when I mation and the destruction of old
heat for every bit of data to be proc proposed that they provide the cor information. The confusion may or
essed. (This is an extremely small rect explanation of Maxwell's demon. may not have existed in Szilard's
quantity of heat: roughly one ten-bil Consider the operating cycle of Szi mind. In most of his paper he refers
lionth of the heat actually generated lard's engine. The last step, in which to measurement as the irreversible
by existing electronic circuits.) the engine's memory is reset to a step, but at one point he makes an ac
In about 1960 Landauer analyzed blank state, is logically irreversible, counting of entropy changes during
the question more thoroughly. He because it compresses two states of the cycle and finds, without explicit
found that some data operations the machine's memory ("The mole ly commenting on it, that the in
are indeed thermodynamically cost cule is on the left" and "The molecule crease in entropy takes place during
ly but. others, including, under cer is on the right") into one ("The mol the resetting of the memory.
tain conditions, copying data from ecule's position has not yet been If subsequent workers had pur
one device to another, are free of any measured"). Thus the engine cannot sued this aspect of Szilard's paper,
fundamental thermodynamic limit reset its memory without adding at they would have come to our present
[see "The Fundamental Physical lim least one bit of entropy to the envi understanding of Maxwell's demon.
its of Computation," by Charles H. ronment. This converts all the work Their failure to do so is an irony in
Bennett and Rolf Landauer; SCIENTIFIC that had been gained in the power the history of science: the advance
AMERICAN,july, 198 5]. stroke back into heat. ment of one branch of physics (the
Landauer's proof begins with the What about the measurement step? quantum theory of radiation) appar
premise that distinct logical states of Is it thermodynamically costly as ently delayed progress in another
a computer must be represented by well? In that case the engine would branch (thermodynamics). One as
distinct physical states of the com add to the entropy of the universe pect of quantum mechanics that re
puter's hardware. For example, ev twice: once in measuring the mole inforced the idea that a fundamental
ery possible state of the computer's cule's position and again in resetting thermodynamic price must ,be paid
memory must be represented by a its memory after the power stroke. for acquiring information is the un
distinct physical configuration (that Actually the measurement does not certainty principle, which holds that
is, a distinct set of currents, voltages, have to be thermodynamically cost certain sets of measurements cannot
fields and so forth). ly. There are ways to observe mole be carried out with more than a cer
Suppose a memory register of n cules other than by bouncing light tain degree of precision. Although
bits is cleared; in other words, sup off them. To prove this point I have the uncertainty principle sounds sim
pose the value in each location is set designed a reversible measuring de ilar to Szilard's hypothesis that meas
at zero, regardless of the previous vice, which measures and records urements have an irreducible entro
value. Before the operation the regis the position of the molecule without py cost, in fact it is fundamentally dif
ter as a whole could have been in any undergoing any thermodynamically ferent. Szilard's hypothesis concerns
of 2n states. After the operation the irreversible steps. the thermodynamic cost of measure
register can be in only one state. The ments, whereas the uncertainty prin
W the demon cannot violate the
operation has therefore compressed e have, then, found the reason ciple concerns the possibility of their
many logical states into one, much as being made at all, whatever their
a piston might compress a gas. second law: in order to observe a thermodynamic cost.
By Landauer's premise, in order to molecule, it must first forget the re Another source of confusion is that
compress a computer's logical state sults of previous observations. For we do not generally think of informa
one must also compress its physical getting results, or discarding infor tion as a liability. We pay to have
state: one must lower the entropy of mation, is thermodynamically costly. newspapers delivered, not taken
its hardware. According to the sec If the demon had a very large mem away. Intuitively, the demon's rec
ond law, this decrease in the entropy ory, of course, it could simply re ord of past actions seems to be a
of the computer's hardware cannot member the results of all its measure valuable (or at worst a useless) com
be accomplished without a compen ments. There would then be no logi modity. But for the demon "yester
sating increase in the entropy of the cally irreversible step and the engine day's newspaper" (the result of a pre
computer's environment. Hence one would convert one bit's worth of heat vious measurement) takes up valu
cannot clear a memory register with into work in each cycle. The trouble able space, and the cost of clearing
out generating heat and adding to the is that the cycle would not then be a that space neutralizes the benefit the
entropy of the environment. Clearing true cycle: every time around, the en demon derived from the newspaper
a memory is a thermodynamically ir gine's memory, initially blank, would when it was fresh. Perhaps the in
reversible operation. acquire another random bit. The cor creasing awareness of environmen
Landauer identified several other rect thermodynamic interpretation tal pollution and the information ex
operations that are thermodynami of this situation would be to say the plosion brought on by computers
cally irreversible. What all these engine increases the entropy of its have made the idea that information
operations have in common is that memory in order to decrease the en can have a negative value seem more
they discard information about the tropy of its environment. natura) now than it would have
computer's past state. In Landauer's Attributing the gain in entropy to seemed earlier in this century.
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