Biology Reference
In-Depth Information
4.9
Info-Statistical Mechanics and the Gnergy Space
Traditionally, the dynamics of any N-particle systems in statistical mechanics is
completely described in terms of the 6-dimensional
phase space
consisting of the
3N positional coordinates and 3N momenta, where N is the number of particles in
the system (Tolman 1979; Prigogine 1980). Unlike the particles dealt with in
statistical mechanics which are featureless and shapeless, the particles of impor-
tance in biology have characteristic shapes and internal structures that determine
their biological properties. In other words, the particles in physics are completely
described in terms of energy and matter (in the phase space) but the description of
the particles in living systems require not only the energy and matter of the particle
but also the genetic information carried by the particle, consistent with the infor-
mation-energy complementarity (or gnergy) postulate discussed in Sect.
2.3.2
.
Thus, it seems necessary to expand the dimensionality of the traditional phase
space to accommodate the
information
dimension, which includes the three
coordinates encoding the
amount
(in bits),
meaning
(e.g., recognizability), and
value
(e.g., practical effects) of information (see Sect.
4.3
). Similar views have
been expressed by Bellomo et al. (2007) and Mamontov et al. (2006). Thus the
expanded “phase space” would comprise the 6N phase space of traditional statisti-
cal mechanics plus the 3N information space entailed by molecular biology.
Therefore, the new space (to be called the “gnergy space”) composed of these
two subspaces would have 9N-dimension as indicated in Eq.
4.31
. This equation
also makes contact with the concepts of
synchronic
and
diachronic
informations
discussed in Sect.
4.5
: It is suggested that the traditional 6N-dimensional phase
space deals with the
synchronic information
defined in Sect.
4.5
and thus can be
alternatively referred to as the
Synchronic Space
while the 3N-dimensional infor-
mation space is concerned with the consequences of history and evolution encoded
in each particle and thus can be referred to as the
Diachronic Space
. The resulting
space will be called the
gnergy space
(since it encodes not only
energy
but also
information
) and represented diagrammatically as shown in Fig.
4.2
.
Gnergy Space
¼
6N-D Phase Space
þ
3N-D Information Space
(4.31)
ð
Synchronic Space
Þð
Diachronic Space
Þ
Figure
4.2
depicts the independence of
genetic information
from
free energy,
which is equivalent to the assertion that that genetic information is not reducible to
the laws of physics and chemistry (see Exclusivity in Sect.
2.3.1
and Statements
4.25 and 4.26). There are many other ways of expressing the same concept, just as
there are many equivalent ways of stating the Second Law of Thermodynamics,
including the following:
1. The genetic information versus free energy orthogonality
2. The independent variations of free energy and genetic information (Statements 4
25 and 4.26)
3. The genetic information versus free energy complementarity
