Page 58 - Introduction to Information Optics

1.6. Trading Information with Entropy 45

operate. The demon is able, we assume, to see every individual molecule, so he
can allow a molecule to pass from one chamber to the other. Now the demon
decides to let the fast molecules in chamber 1 pass into chamber 2, and the
slower molecules in chamber 2 to pass into chamber 1. In this manner we
eventually are able to collect all the fast molecules in one chamber and all the
slower molecules in other chambers. Thus, without any expenditure of work,
the demon is able to raise the temperature in one chamber and lower the
temperature in the other. Hence, work can be performed by the difference in
temperature between the two chambers. However, in a thermally isolated
chamber, this radiation within the chamber is only black body radiation, and
it is impossible for the demon to see anything inside the chamber. Raising the
temperature of the chamber would not help, since the demon would be able to
see only the thermal radiation and its random fluctuations, but not the
molecules. Thus, under these isolated conditions, the demon is unable to
operate the trapdoor.
In order for the demon to see the individual molecules, we can provide the
demon with a fresh flashlight (i.e., the source of negentropy or information),
Then, by using the amount of information provided by the flashlight, the
demon is able to operate the trapdoor. In this manner he can decrease the
entropy of the chamber to a lower state. However, the entropy increase in the
flashlight can be shown to be larger than, or at least equal to, the entropy
decrease in the chamber. The lowest entropy increase by the flashlight can be
seen as

AS ;/ = y, (1.141)

where h is Planck's constant v is the frequency of the flashlight radiation, and
T 0 is the temperature of the chamber in degrees Kelvin. The corresponding
amount of information provided for the demon is

AS,
'< = - (L142 >

(we assume that the demon is capable of absorbing this information). By using
this data the demon is able to reduce the chamber entropy from S 0 to S, and
then the amount entropy decreased per down operation at best would be

AN AN
—, for — «1, (1.143)