Ts. D. TSVETKOV, G. PETROV and P. TSVETKOVA

*Institute for Cryobiology and Food Technologies, BG - 1407 Sofia, Bulgaria*

TSVETKOV, Ts. D., G. PETROV and P. TSVETKOVA, 2005. Non equilibrium thermodynamics by the concrete quantum field systems in the cellular cryobiology and anhydrobiology. *Bulg. J. Agric.* *Sci., *11: 387-403

The feature of the contemporary theoretical biological physics in the cryobiology (the study of the structure of living cells and systems at very low temperatures) and anhydrobiology (the study of the structure of living cells and systems at low water contents) is in common. The question above the possibility to find the complicate appearances connected with the existence of the life and the living systems his place in the mathematical frame of any one concrete quantum field theory by the contemporary state of the theoretical biological physics is open by the consideration of high topographical complementarities by the London-force interactions involved importantly in the highly specific and strong but purely physical complexing of enzymes with substrates, of antigens with antibodies, etc. From the new results by the contributions of the environmental freezing-drying and vacuum sublimation (Zwetkow, 1985; Tsvetkov et al., 1989).it is hopped that by the grate form expressed e.g. by the thermodynamically behaviour of the living cells and systems will be possibly to describe the biological expressions by means of concrete quantum field system too. From a grate interest is the so called problem of the connection between the entropy and the time arrow. With other words the connection between the entropy and the causality according to quantum field theory of the interactions between a quantum field system and external classical field modelled by the additional boundary conditions.

It is knowing that one of the major causes of damage produced by the several effects at cellular level: (i) low temperatureper se, (ii) direct effects of freezing and (iii) indirect effects of freezing and (iv) the biochemical modifications in the structure of the living cells by the lipids, phospholipids, proteins in the cell membrane formed by interacting of the "matter" fields such as a new electron distribution or the protonisation at a given time for the living cells and systems is freezing induced dehydration at very short distance scales, where various properties of the physical vacuum of any one concrete quantum field system for which the vacuum state must be conformed by means of additional boundary conditions are of crucial importance.

The contemporary methods of the theoretical biological physics are this used in the quantum mechanical problems of the many bodies. The several results obtained over there can be related without every changing in the quantum field theory applied to the biological physics e.g. biological dynamic too. The only deep difference consist in this field is that the physics of the many bodies proceed from canonical quantization and the existence of the distance interacting force, while the relativistic quantum field theory proceed from local interaction and in consequence of the non canonical quantization. In every problem where this difference is not essential the methods of physics of many bodies can be related to the relativistic quantum field theory too. By the concrete local quantum field system the physical state from the asymptotical part can be subtracted theoretically by the diagonalisation of the S-matrices in the case of the non canonical quantisation and the choice of so one states for which the diagonal elements in the absolutely amount are equal to one. It is possibly tat in this processes in the theory will be introduced an elements of the non locality (similar to the Coulomb forces in the Quantum electrodynamics and the Casimir force by the interaction of the quantum electromagnetic field with the classical objects or the so called string objects in the Quantum chromo dynamics)). On essential result of the perturbation theory in the relativistic quantum fields is the importance of the non local operators expansion on the light cone in the concrete quantum field system describing by the Quantum chromo dynamics. This can be understood by means of the consideration of the causality conditions for the invariance amplitudes and structure functions in the sense of the S-matrix theory for a concrete quantum field system in the deep inelastic scattering of the electron proton scattering e.g. where the concrete quantum field system is hopped to be described by the Quantum chromo dynamic (Bogolubov et al., 1976).
The basic theoretical entity - the concrete quantum field system as an object of the quantum field theory is considered as relativistic quantum statistical system with infinitely many degrees of freedom by means of any one biological system (e.g., the ion-ion "salt linkages"). A system of the local interacting relativistic quantum fields with the classical objects is then analogous to a complicated concrete relativistic quantum field system in biological physical dynamics. It can exist in different energy states, namely the ground state and various excited states. The excited states of the field system are characterized by the presence of the excitation quanta, which are the particles (electrons, quarks, photons ...) from which our material world is composed. In the ground state of the relativistic quantum field system there are no excitation quanta, and hence no particles, present; the vacuum is this ground state of the quantum "force" and the quantum "matter" fields. Consequently, different features of the physical vacuum for any concrete quantum field system may be modelled by means of the ground states of various biological systems. For example, the ground state of the new electron distribution of the molecular crystal and molecules of the cell models the electromagnetic vacuum, a semiconductor model the Dirac vacuum, and relativistic superconductor may model aspects of the vacuum as regard the strong nucleon and weak force. The properties and the structure of the vacuum are involved by the discussions of the many phenomena as for example, spontaneous emission and the Lamb shift or the Casimir effect for perfect and not perfect conductors, the origin of the mass for the W and Z bosons and the confinement of the quarks, pair creation, new electron distribution created by the heavy ion-ion collision and the charge by the polarization or the zero point energy of the vacuum and may be for the vitrification of the living cells as a changing of the non stability state of the cells water in to stabile by means of the same structure and the ultra structure of the life cells from the point of view in the theoretical biological physics for the cellular cryobiology and anhydrobiology.

The Casimir effect (Bordag et al., 1984) for perfect conductors, and Petrov (1989) for not perfect conductors) is calculated by the help of quantum field methods as one of the fundamental effects of Quantum Field Theory. It tests the relevance of the zero point energy: the system of two moved with a constant velocity v to each other parallel, large conducting plates in a distance at a given time t = t_{0} in the Minkowski space changes the vacuum energy of Quantum Electrodynamics in such a way, that a net attractive force between the plates results. Qualitatively, this situation does not change, if the system is at finite temperature or with other words has a thermodynamic behaviour of any one concrete relativistic quantum field system and the new point at this time is an asymptotical stabile centre of the localisation of this quantum field described by the Banach valued vector state defined in this observable point of the Mincowski space-time. Wentzel (1941,1942) has at the first turned one's attention to the possibly role by the energy of the zero fluctuations for the forming of the forces from the field interactions.

At the molecular level (Mitter and Robaschik, 1999) the thermodynamic behaviour is considered by any concrete quantum field system with additional boundaries as by the Casimir effect between the two parallel, perfectly conducting square plates (side L, distance d, L > d), embedded in a large cube (side L) with one of the plates at face an periodic boundary condition. It is considered contributions from the volume L^{2}d between the plates resp. L^{2}(L-d) outside have different temperature (outside T', inside T). For the temperatures T' < T, the external pressure is reduced in comparison with the standard situation (T' = T). Therefore it is expected the existence of a certain distance d_{0}, at which the Casimir attraction is compensated by the net radiation pressure. That is possibly to investigate this field equilibrium point for this system or for hydro-logical equilibrium of the system membrane-solutions-water and its stability both for an isothermal and an adiabatic treatment of the interior region.