A better grasp of the physical foundations of life is necessary before we can understand the processes occurring inside a living cell. In his physical theory of the cell, American physiologist Gilbert Ling introduced an important notion of the resting state of the cell. He describes this state as an independent stable thermodynamic state of a living substance in which it has stored all the energy it needs to perform all kinds of biological work. This state is characterised by lower entropy of the system than in an active state. The main contribution to this reduction in entropy is made by the cellular water (the dominant component with a concentration of 14 M) which remains in a bound quasi-crystallised state in a resting cell. When the cell becomes active the water gets desorbed and the system's entropy goes up sharply while the free energy of the system decreases as it is used up for biological work. However, Ling's approach is primarily qualitative in terms of thermodynamics and it needs to be characterised more specifically. To this end, we propose a new thermodynamic approach to studying Ling's model of the living cell (Ling's cell), the centrepiece of which is the non-ergodicity property which has recently been proved for a wide range of systems in statistical mechanics [7]. In many ways this new thermodynamics overlaps with the standard quasi-stationary thermodynamics and is therefore compatible with the principles of the Ling cell, however a number of new specific results take into account the existence of several non-trivial motion integrals communicating with each other, whose existence follows from the non-ergodicity of the system (Ling's cell). These results allowed us to develop general thermodynamic approaches to explaining some of the well-known physiological phenomena, which can be used for further physical analysis of these phenomena using specific physical models.

In this paper we prove that Bose gas with weak pair interaction is non ergodic system. In order to prove this fact we consider the divergences in some nonequilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of renormalization of such divergences and illustrate it with some simple examples. The fact that the system is non ergodic leads to the following consequence: to prove that the system tends to the thermal equilibrium we should take into account its behavior on its boundary. In this paper we illustrate this thesis with the Bogoliubov derivation of the kinetic equations.2000 MSC: 81Q30 (Feynmann integrals and graps) * Institute of Spectroscopy, RAS 142190 Moskow Region, Troitsk, prokhordv@yandex.ru Dedicated to the memory of my father V.D. Prokhorenko.

We investigate the structure of Kubo -Martin -Schwinger (KMS) states on some extension of the universal enveloping algebra of SL(2, C). We find that there exists a one-to-one correspondence between the set of all covariant KMS states on this algebra and the set of all probability measures dµ on the real half-line [0, +∞), which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.

For a wide class of Hamiltonians used in quantum field theory and statistical physics, we obtain an explicit formula describing the behavior of the vacuum expectation of the evolution operator on large, but finite, time intervals. This formula also holds for processes with unstable states.