4 Some Biochemical Reflections on Information and Communication
93
and the classical canonical form J defined by J (m−1) = 0; J (m) = 0
J =
⎛
⎜
⎜
⎜
⎜
⎝
0 1 0 · 0
0 0 1 · ·
· · · · 0
· · · · 1
0 · · · 0
⎞
⎟
⎟
⎟
⎟
⎠
(4.21)
are similar through the unitary transformation
Q = B
−1 J B
|hB
−1
= |f = |f 1 , f 2 , . . . , f m .
(4.22)
In terms of the basis |f one can finally rewrite Eq. (4.19) in classical canonical
form
Γ
(2)
T = λ L J
(m−1)
+ λ S J ; J =
m−1
k=1
|f k f k+1 |
(4.23)
with
E = Tr
H 2 Γ
(2)
T
= 0.
(4.24)
Looking back, we have in fact carried out a sequence of steps, i.e. complex
scaling and localized thermal fluctuations leading up to two orthogonal many-body
functions, Ψ (g) and Ψ (g ∗ ), see Eq. (4.9) above. Thus the degenerate structure characterized by Eq. (4.23) is in actual fact not a standard quantum mechanical state as
it does represent more accurately a sequence of successive transitions. It is an open
spatio-temporal structure, which does not exist under a certain minimum “size” and
lifetime, see Refs. [19, 24], with anomalous time evolutions and, as will be demonstrated below, subject to a (cumulative) Poisson-like statistics. A final attribute of
far-reaching importance is the factorization property of transformation B as displayed in Eq. (4.12).
Appendix B: Time Evolution of the STN Configuration
As portrayed in the central part of the text there are many distinct realizations of
STN structures to amorphous condensed matter in general and biological, complex
enough systems in particular [11–13, 19, 24]. For instance describing cellular interactions and their various properties and differentiation, it is convenient to model
each cell as an STN entity, based on tunneling proton pairs (quasibosonic degrees
of freedom) as sites for the preferred basis. The dimension of the STN organization gives rise to a particular transformation B = B m where the associated factorizing structure of the vectors exhibits nested encoded programs, e.g. the genetic- and
higher level codes, as will be pursued in the main script.
93
and the classical canonical form J defined by J (m−1) = 0; J (m) = 0
J =
⎛
⎜
⎜
⎜
⎜
⎝
0 1 0 · 0
0 0 1 · ·
· · · · 0
· · · · 1
0 · · · 0
⎞
⎟
⎟
⎟
⎟
⎠
(4.21)
are similar through the unitary transformation
Q = B
−1 J B
|hB
−1
= |f = |f 1 , f 2 , . . . , f m .
(4.22)
In terms of the basis |f one can finally rewrite Eq. (4.19) in classical canonical
form
Γ
(2)
T = λ L J
(m−1)
+ λ S J ; J =
m−1
k=1
|f k f k+1 |
(4.23)
with
E = Tr
H 2 Γ
(2)
T
= 0.
(4.24)
Looking back, we have in fact carried out a sequence of steps, i.e. complex
scaling and localized thermal fluctuations leading up to two orthogonal many-body
functions, Ψ (g) and Ψ (g ∗ ), see Eq. (4.9) above. Thus the degenerate structure characterized by Eq. (4.23) is in actual fact not a standard quantum mechanical state as
it does represent more accurately a sequence of successive transitions. It is an open
spatio-temporal structure, which does not exist under a certain minimum “size” and
lifetime, see Refs. [19, 24], with anomalous time evolutions and, as will be demonstrated below, subject to a (cumulative) Poisson-like statistics. A final attribute of
far-reaching importance is the factorization property of transformation B as displayed in Eq. (4.12).
Appendix B: Time Evolution of the STN Configuration
As portrayed in the central part of the text there are many distinct realizations of
STN structures to amorphous condensed matter in general and biological, complex
enough systems in particular [11–13, 19, 24]. For instance describing cellular interactions and their various properties and differentiation, it is convenient to model
each cell as an STN entity, based on tunneling proton pairs (quasibosonic degrees
of freedom) as sites for the preferred basis. The dimension of the STN organization gives rise to a particular transformation B = B m where the associated factorizing structure of the vectors exhibits nested encoded programs, e.g. the genetic- and
higher level codes, as will be pursued in the main script.