Page 27 - 2020SEP30 Brief Booklet C

ON THE DECREASE ENTROPY 303
OF

faculty, in the sense that one can recognize However, it is no longer constraincd to the
by the state parameter y what value another upper part of the cylinder but bounces inany
state parameter z had at an earlier moment, times against the piston which is already
and we shall see that simply because of such moving in the lower part of the cylinder. In
a memory the Second Law would be vio- this way the molecule does a certain amount
lated, if the measurement could take place of work on the piston. This is the work that
without compensation. We shall realize that corresponds to the isothermal expansion of
the Second Law is not threatened as much an ideal gas--consisting of one single mole-
by this entropy decrease as one would think, cule-from volume V, to the volume
as soon as we see that the entropy decrease V1 + V2 . After some time, when the piston
resulting from the intervention would be has reached the bottom of the container, the
compensated completely in any event if the molecule has again the full volume V1 + Vz
execution of such a measurement were, for to move about in, and the piston is then re-
instance, always accompanied by produc- moved. The procedure can be repeated as
tion of k log 2 units of entropy. In that case many times as desired. The man moves the
it will be possible to find a more general piston up or down depending on whether the
entropy law, which applies universally to all molecule is trapped in the upper or lower half
measurements. Finally we shall consider a of the piston. In more detail, this motion
very simple (of course, not living) device, may be caused by a weight, that is to be
that is able to make measurements con- raised, through a mechanisni that transmits
tinually and whose “biological phenomena” the force from the piston to the weight, in
we can easily follow. By direct calculation, such a way that the latter is always dis-
one finds in fact a continual entropy produc- placed upwards. In this way the potential
tion of the magnitude required by the above- energy of the weight certainly increases
mentioned more general entropy law de- constantly. (The transmission of force to the
rived from the validity of the Second Law. weight is best arranged so that the force
The first example, which we are going to exerted by the weight on the piston at any
consider more closely as a typical one, is the position of the latter equals the average
following. A standing hollow cylinder, closed pressure of the gas.) It is clear that in this
at both ends, can be separated into two manner energy is constantly gained at the
possibly unequal sections of volumes V, and expense of heat, insofar as the biological
V, respectively by inserting a partition from phenomena of the intervening nian are ig-
the side at an arbitrarily fixed height. This nored in the calculation.
partition forms a piston that can be moved In order to understand the essence of the
up and down in the cylinder. An infinitely man’s effect on the system, one best imagines
large heat reservoir of a given temperature T that the movement of the piston is performed
insures that any gas present in the cylinder niechanically and that the man’s activity
undergoes isothermal expansion as the consists only in determining the altitude of
piston moves. This gas shall consist of a the molecule and in pushing a lever (which
single molecule which, as long as the piston steers the piston) to the right or left, depend-
is not inserted into the cylinder, tumbles ing on whether the molecule’s height requires
about in the whole cylinder by virtue of its a down- or upward movement. This nieans
thermal motion. that the intervention of the huniari being
Imagine, specifically, a man who at a given consists only in the coupling of two position
time inserts the piston into the cylinder and co-ordinates, namely a co-ordinate x, which
somehow notes whether the molecule is determines the altitude of the molecule, with
caught in the upper or lower part of the cyl-
inder, that is, in volume V1 or V,. If he another co-ordinate y, which determines the
should find that the former is the case, then position of the lever and therefore also
he would move the piston slowly downward whether an upward or downward motion is
until it reaches the bottom of the cylinder. imparted to the piston. It is best to imagine
During this slow movement of the piston the the mass of the piston as large and its speed
molecule stays, of course, above the piston. sufficiently great, so that the thermal agita-