Page 60 - Introduction to Information Optics

1.6. Trading Information with Entropy 4 3

With this amount of information gain, the demon is able to reduce the entropy
of the chamber to a lower state. Again we can show that the overall net entropy
changed in the chamber, per trapdoor operation, by the demon, would be

AN
AS = A/ln 2 >0, (1.149)

in which we see that the diffraction-limited demon's exorcist is still within the
limit of the second law of thermodynamics.

1.6.2. MINIMUM COST OF ENTROPY

One question still unanswered is, What would be the minimum cost of
entropy required for the demon to operate the trapdoor? Let the arrival
molecules at the trapdoor at an instant be one, two, or more molecules. Then
the computer is required to provide the demon with a "yes" or a "no"
information. For example, if a single molecule is approaching the trapdoor
(say, a high-velocity one), the demon will open the trapdoor to allow the
molecule to go through. Otherwise, he will stand still.
For simplicity, let us assume that the probability of one molecule arriving
at the trapdoor is a 50% chance; then the demon needs one additional bit of
information from the computer for him to open the trapdoor. This additional
bit of information corresponds to the amount of entropy increased provided
by the computer; i.e.,

&S p = k\n2xQ.lk, (1.150)

which is the minimum cost of entropy required for the demon to operate the
trapdoor. Thus, the overall net entropy increased in the chamber is

>0. (1.151)

If one takes into account the other bit of "no" information provided by the
computer, then the average net entropy increased in the chamber per operation
would be

in which two quantas of light radiation are required. It is trivial, if one includes