Page 59 - Introduction to Information Optics

44 1. Entropy Information and Optics
where N 0 and AN denote the initial and the net change in complexity of the
chamber.
However, from the second law of thermodynamics, the net entropy increase
in the isolated chamber should be

kv AJVl
AS = >0. (1.144)
0]
So we see that the amount of entropy provided by the flashlight is higher than
the amount of the chamber entropy that the demon can reduce.
Since we are in the computer era, we further assume that the demon is a
diffraction-limited demon. Even though we assume that the demon can see the
molecules under constant temperature conditions, he is so diffraction limited
that he cannot distinguish an individual molecule from a group of molecules
that are approaching the trapdoor. In order for him to do so, we equip the
demon with the most powerful computer ever developed. To perceive the
arriving molecules, the demon turns on the flashlight, which is required to emit
at least a quanta of light to make the observation, i.e.,

hv = kT. (1.145)

We also assume that the quanta of light reflected by the approaching molecules
is totally absorbed by the diffractive-limited eye of the demon, which corre-
sponds to an increase of entropy in the demon; that is,

AS d = —, (1.146)

or equivalent to the amount of information provided to the demon; i.e.,

^ = rrv ( L147 >
kin 2

Because of the diffraction-limited eye, the demon needs to process the absorbed
quanta to a higher resolution, so that he is able to resolve the molecules and
to allow the passages of the fast or slower molecules through the trapdoor. The
amount of information gain, through the processing by the equipped computer,
constitutes an equivalent amount of entropy increased, as given by

AS p = kAI d In 2, (1.148)
where A/ d is the incremental amount of information provided by the computer.