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where H O is the Shannon entropy of the machine outputs, H E is the Shannon
entropy of the environmental inputs, and H M is the Shannon entropy of the state
of the machine or its controller. Two cautionary remarks are in order concerning
Inequality 5.66 :
1. The symbols for Shannon entropy, H, should not be confused with the symbol
for enthalpy, H, in thermodynamics, and
2. The same term “entropy” is represented by H in information theory and by S in
thermodynamics. In other words, there are two kinds of entropies - the informa-
tion-theoretic entropy (referred to by some as “intropy”) and thermodynamic
entropy. There are two schools of thought about the relation between intropy, H,
and entropy, S (Sect. 4.7 ). One school led by Jaynes (1957a, b) maintains that H
and S are in principle identical up to a constant factor, whereas the other schools
represented by Wicken (1987), myself (Ji 2004c), and others assert that H and S
are distinct and cannot be quantitatively related (see Sect. 4.7 ) .
Just as the Second Law of thermodynamics can be stated in many equivalent
ways, so LRV can be expressed in more than one ways, including the following:
Simple machines cannot perform complex tasks . (5.67)
To accomplish a complex tasks, it is necessary to employ complex machines. (5.68)
Nature does not employ complex machines to accomplish simple tasks. (5.69)
If the internal structure of a biological machine is found to be complex, it is very likely that
the task performed by the machine is complex.
(5.70)
Thus, LRV provides one way to explain the possible biological role of the
complex biological structures such as signal transduction pathways,
transcriptosomes, nuclear pore complexes, both of which can implicate 50 or
more proteins (Halle and Meisterernst 1996; Dellaire 2007). For example, it is
possible that nuclear pore complexes had to increase the variety of their internal
states to maintain functional homeostasis (e.g., transport right RNA-protein
complexes in and out of the nuclear compartment at right times and at right speeds)
in response to increasingly complexifying environmental (e.g., cytoplasmic) inputs
or perturbations. In other words, nuclear pore complexes (viewed as molecular
computers or molecular texts) had to become complex in their internal structures so
as to process (or carry out computations on) more and more complex input signals
from their microenvironment in order to produce the desired outputs without fail.
5.3.3 Principles of After-Demand Supply (ADS)
and Before-Demand Supply (BDS)
There are three distinct ways for a system to interact with its environment or three
distinct types of supply and demand: (1) The system adjust its internal states in
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