Biology - Molecular Theory of the Living Cell - page 100

Fig. 4.2 The gnergy space . The gnergy space comprises two complementary subspaces - the
6N-dimensional phase space (or the synchronic space ) and the 3N-dimensional information space
(or the diachronic space ). Energy here refers to free energy, which is a function of both internal
energy E and system entropy S. Here, physical entropy S is presumed to be fundamentally different
from Shannon's entropy, H, in agreement with Wicken (1987) but in contradiction to the
information theory of Brillouin (1953, 1956) (see Table 4.3 ). For a review of this controversial
field, see (Leff and Rex 1962) and (Ji 2006d). Information has three dimensions: a ¼ amount,
m ¼ meaning, and v ¼ value. Only the quantitative aspect of information, namely, a , is captured
by Shannon entropy (see Sect. 4.3 ). The time evolution of an N-particle system traces out what
may be referred to as a semi-stochastic trajectory in the gnergy space which projects a stochastic
shadow onto the phase space and a deterministic shadow onto the information space. It should be
noted that the trajectories shown above represent the averages of their corresponding ensembles of
trajectories (Prigogine 1980). “Stochastic” processes are the apparently random processes that
exhibit regularities although not predictable. Deterministic processes exhibit properties that are
predictable
It is suggested here that, to study the dynamics of living systems such as
genome-wide kinetics of mRNA levels measured with DNA microarrays (Watson
and Akil 1999), treated as N-particle systems, it is necessary to employ the gnergy
space. Since living systems trace out trajectories that are both stochastic and
deterministic (see the legend to Fig. 4.2 for the definitions of “stochastic” and
“deterministic”), the study of living processes in the gnergy space has been referred
to as the info-statistical mechanics (Ji 2006a)
The orthogonality between information and free energy depicted in Fig. 4.2 may
be described in yet another way, using the photosynthetic process as an example.
Figure 4.3 shows the complex interactions among light , chemical reactions , heat ,
evolution , and catalysis in producing the phenomenon of life.