Biology Reference
In-Depth Information
information into tangible effects. The information theory as applied to cell biology
entails elucidating the molecular mechanisms of the following set of processes:
1. A hormone carries information to a cell.
2. The cell recognizes the hormone through its receptor.
3. The cell transduces the information carried by the messenger into a form that can
be recognized by intracellular effector mechanisms.
4. The effector mechanism is activated to produce tangible consequences (e.g.,
expression of a set of genes) controlled by the information received.
5. All the enzymes inside a cell can be treated as “elementary quantum computers”
(analogous to the silicon chips in man-made computers) whose interactions are
organized in space and time, and the cell itself can be viewed as the
smallest
autonomous quantum computer
powered by the free energy released fromchemical
reactions that store, transform, and utilize qubits to perform quantum computation.
4.7 The Information-Entropy Relations
Equation
4.4
is helpful in clarifying the theoretical relation between
information
and
entropy
, which has been the focus of debates in recent decades (Ji 2006d). On
the basis of Eq.
4.4
, it is possible to deduce the following conclusion:
Information and Shannon entropy are not identical.
(4.22)
Statement 4.22 is consistent with Statement 4.5. I believe, in agreement with
Wicken (1987), that Shannon entropy, H, given by Eq.
4.3
and thermodynamic
entropy, S, given by Eq.
4.23
below, are not the same despite their similar
mathematical formulas, only accidentally sharing the common name
entropy
:
¼
S
k
B
logW
(4.23)
where k
B
is the Boltzmann constant and W is the number of microstates (or
molecular states) compatible with the observed macrostate of the thermodynamic
system under consideration. The nonidentity between H and S expressed in State-
ment 4.22 can be transformed into Statement 4.24 without losing validity:
Information defined by Shannon and thermodynamic entropy are not quantitatively related.
(4.24)
For convenience, we may refer to Statement 4.22 as the Principle of Non-identity
of Information and Shannon Entropy (PNISE) and Statement 4.24 as the Principle of
the Non-identity of Information and Thermodynamic Entropy (PNITE). Further-
more, since thermodynamic entropy, S, is a part of free energy (see Eq.
2.1
), we can
generalize Statement 4.24 by replacing “thermodynamic entropy” with “energy” to
generate Statement 4.25:
Information and energy are not quantitatively related.
(4.25)
