Alexandre V. Boukalov

e-mail: boukalov@gmail.com
The Centre of Physical and Space Researches, International Institute of Socionics
"Physics of Consciousness and Life, Cosmology and Astrophysics" journal, issue 4, 2002 .

On the quantity of information in alive organisms
and degree of order

The existence of metric, temporal analog of thermodynamics, named tempodynamics, follows from the consideration of the degree of order of alive organisms. In tempodynamics the entropy and information are determinated by the quantity of the temporal microscopic states of object. The estimations of quantity of information and degree of order are given for the alive organisms: a cell, a man, a biosphere, and the biomass of the Universe. It is shown the considerable quantitative difference between a whole organism and an aggregate of the separate cells for alive with the same mass.
Key words: thermodynamics, tempodynamics, physics of life, informational ordering of alive organisms, cell, human, biosphere, biomass of the Universe.

In our previous communication it was shown [2] that the degree of the alive matter order prevails compared with the one of the Universe lifeless matter:
.

As far as this order is connected with the metrics, dynamics, time degrees of freedom, we can conclude that it means the quantity of the temporal (metrics) degrees of freedom per one thermal degree� of freedom of alive matter:
,
where I_t = t_k lnw_t �is the temporal information and entropy, S_t+I_t=const. This degree of order is connected with the presence of a set of the dynamics degrees of freedom in an organism.
,     (1)
where w_t is the quantity of microstates of the time (temporal) degrees of freedom of alive organism, Δt_k=Δt_bio≥ ħ / (2kT); Δt_k=1.27·10^-14sec under T=300�.

Formula (1) is analogous to the earlier obtained formula for the information quantity in alive nature in terms of energetical equivalent per one time (temporal) degree of freedom:
.     (2)

There is no surprise in these formulae equivalence; because, for example, in the quantum mechanics under the matter structure description the space-time and energy-impulse presentations are equal and symmetrical. Under the mentioned description it follows from the formula (1) the existence of the metrics, space-time analogy of thermodynamics, which can be called the tempodynamics. In the tempodynamics the entropy and information are determined by the quantity of the time and space� microstates of object. The information quantity in the action� space, where the Planck constant is the quantum, can be written in a first approximation by the following expression:
I_s^*= I_kT ·I_t=kT lnw_kT Δt_k lnw_t= ħ lnw_kT lnw_t=ħ lnw_s^*.     (3)

In such a formula the time and energetical degrees of freedom are independent. So for as the action space is a unite, the energetical and temporal microstates are connected in it. Since w=P!≈P^P, the connected microstates quantity in the action space makes up:
w_s=(P_t·P_kT)! .    (4)

Thus it is more correctly to describe the information quantity in the acton space by the following formula:
I_s= kT·Δt_k ln((P_t·P_kT)!)=ħ lnw_s .     (5)

Then the dimensionless information quantity is determined by the derivative of I_s with respect to S_n and described by the formula:
    (6)

We have obtained earlier [2] the formulae for the quantity of energy, passing through alive organism per time t=N·Δt_k:

The correspondent action makes up:
    (7)

Formula (7) is more approximated compared with (5) one. Taking into account that the Universe biomass quantity corresponds to
,    (8)
the quantity of the equivalent aminoacid residuals and nucleotypes is N~10^58�59. Then the information quantity per time, near to the Universe existence time [4] t₀ =1 / H₀ = 4.48·10¹⁷�≈10^31.5Δt_k, is obtained from (5) by the following way:
,     (9)
where I_U=6·10¹²⁴ is the Universe information quantity [3].

For the Earth biosphere and for an analogical one with the mass
 �and     (10)
the information quantity makes up:
    (11)

For a separate plant or animal cell with the molecule mass 10^14-15, the correspondent aminoacid residual quantity N_pt ≈10^11-12�and the division time t~10^3–4s=10^17-18Δt_k
.    (12)

For the cell line with the generation quantity n=t₀/t ≈ 10¹⁷/10⁴≈10¹³ the degree of order makes up:
.    (13)

For the human alive organism with t~2,2·10⁹c~10²³Δt_k the degree of order could be
.    (14)

Such an approach is valid only under the consideration of organism as a set of the undifferent cells.

Now let us consider the difference of an organism and a set of cells of the same mass and quantity. For a set of N_c separate cells
.     (15)

For the plant organism, consisted with N_c cells, ordered in the functioning structure, the information quantity can be valued by the formula:
.     (16)

Thus the plant organism degree of order prevails by some dozens (N_z~50) compared the one for the set of separate plant cells. The animal organism degree of order, taking into account the additional degrees of freedom, connected with the organism cells differentiation, makes up
  ,    (17)
where, basing on the data [5],
.

For human civilization with the maximal possible people quantity (~1.5·10¹⁰ persons) the degree of order is comparable with the one for the biosphere. The correspondent total mass of the maximal Earth human population will makes up:
,    (18)
where N_y = 4.5·10¹⁵kg / 8·10¹¹kg = 5.62·10³.

Then the human organism degree of order compared with the set of separate cells makes up:
.     (19)

The human organism degree of order, basing on (17), makes up:
.    (20)

Note that the obtained Planck cells quantity for human organism equals to the cosmological number which is the barions number in Universe. It proves the certain structural resonance of human organism in Universe.

The degree of order of the human civilization, consisting with 1.5·10¹⁰ persons per time t~t₀, makes up

The obtained results conform to the intuitive perception of human organism as a more ordered object compared with the set of separate cells. Note, that the previous thermodynamical approach did not provide to make difference between the alive and lifeless structures [1], without the consideration of more detailed differences between cells and organisms.

The nearness between the degree of order for the developed human civilization and the one for whole Earth biosphere shows the human factor global role in the biosphere. This notion is in agreement with the conclusion, made by many researchers, beginning from V. I. Vernadskiy, about the decisive influence of modern civilization on the Earth biosphere, whereas this influence can be constructive and destructive as well.

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