Physics - Molecular Theory of the Living Cell - page 12

where S A and S B refer to the absolute entropy contents of thermodynamic systems
A and B, respectively, or two different sates of a given thermodynamic system,
A being the final and B the initial states.
It is important to distinguish between an absolute value and a differential one ,
because conflating these two kinds of values can lead to paradoxes. For example,
RNA levels in a cell are differential values that are determined by the balance
between two opposing processes, RNA synthesis (or transcription) and RNA
degradation, whereas the RNA level in a test tube without RNA degrading enzymes
would be an absolute entity. Not distinguishing between these two distinct RNA
entities have led to numerous errors in interpreting DNA microarray data since the
mid-1990s (see Chap. 12 ) (Ji et al. 2009a). Similarly, conflating “entropy” (an
absolute entity) and “entropy change” (a differential entity) can be viewed as the
root cause for Schr˝dinger's paradox, Statement 2.14.
It would be convenient to adopt the term “negentropy” first introduced by
Brillouin in 1953 to formally (or syntactically) represent either “negative entropy
(NE)” (an absolute entity) or “negative entropy change (NEC)” (a differential
entity). Since, physically (or semantically), NE does not exist, “negentropy” by
default would stand for “negative entropy change.” Using “negentropy” in this
carefully defined sense, we can formulate Statement 2.18 which is physically
meaningful:
Negentropy is a measure of order. (2.18)

The seemingly contradictory Statements 2.13 and 2.18 can be combined into one
true statement as shown below:
Negentropy defined as “negative entropy change” can, but negentropy defined as “negative
entropy” cannot, be a measure of order. (2.19)
It may be convenient to refer to Statement 2.19 as the negentropy principle of
order (NPO).
There may be many situations similar to Schro ˝ dinger's paradox, Eq. 2.10 . Two
examples are (1) Maxwell's Demon , and (2) Brillouin's NPI (Negentropy Principle
of Information):

1. Maxwell introduced his famous demon in 1871 (Brillouin 1951):

He will, thus, without expenditure of work raise the temperature of B and lower that of A,
... . (2.20)
It is asserted here that Statement 2.20 is an example of Schro˝dinger's paradox ,
because it contains a phrase that is syntactically (or formally) sound but physically
(or semantically) meaningless in view of the fact that the Second Law prohibits
changing temperatures without dissipating free energy (i.e., without expending
work ). Thus, it may be concluded that Maxwell's demon cannot exist or violates
the Second Law.