The Significance of Non-ergodic Property of Statistical Mechanics Systems for Understanding Resting State of a Living Cell

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 characterized 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-crystallized 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 ofh thermodynamics and it needs to be characterized 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 off which is the non-ergodicity property which has recently been proved for a wide range of systems in statistical mechanics (Prokhorenko, 2009). 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 nonergodicity 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.