Page 57 - Introduction to Information Optics

42 1. Entropy Information and Optics

corresponds to some complexity of a structure but not the maximum, and if S 0
remains constant (AS 0 = 0), then after a certain free evolution without the
influence of external sources, from Eq. (1.138), we will have

A/^0, (1.139)

since AS,, = 0.
In view of the preceding equation, we see that the changes in information A/
are negative, or decreasing. The interpretation is that, when we have no a priori
knowledge of the system complexity, the entropy S 0 is assumed to be maximum
(i.e., the equiprobable case). The information provided by the system structure
is maximum, therefore, A/ ^ 0 is due to the fact that the system entropy has
to increase AS,, > 0. In other words, a decrease of information is needed in the
system for its entropy to increase. This means that information can be provided
or transmitted (a souce of negentropy) only by increasing the entropy of the
system. However, if the initial entropy S 0 is at a maximum state, then A/ = 0
which implies that the system cannot be used as a source of negentropy (or
information). Thus, we see that information and (physical) entropy can be
simply traded,

A/ <± AS. 1.140)

1.6.1. DEMON EXORCIST

One of the most interesting applications of the entropy theory of informa-
tion must be the Maxwell's Sorting Demon, for which we consider a thermally
isolated chamber as shown in Fig. 1.15. The chamber is divided into two
chambers by a partition wall equipped with a small trapdoor for the demon to

THERMALLY INSULATED
Fig. 1.15. Operation of Maxwell's demon.