In the connection with our research into non–equilibrium kinetics mentioned above, there appeared unsolved conceptual problems concerning temperature. This central concept of thermal physics widely used in technology and sciences, is one of the most frequently employed physical quantity in common praxis. Operative methods of the temperature measurement are described in detail in various practical instructions and textbooks, however, paradoxically, the systematic and logically rigorous treatment of this physical quantity is almost lacking in the current literature. It was thus necessary to re-examine this fundamental concept of thermal physics from the logical, epistemological and mathematical point of view. Besides, we also reopened an interesting problem of relativistic transformation of temperature. There exists, namely, long-lasting controversy among different approaches to this question, generally known as Planck-Ott imbroglio. Various, mostly unsuccessful, attempts to solve this demanding problem using a combinations of tools of classical thermodynamics, transformation rules of special relativity, theory of black-body radiation and kinetic theory, were reviewed. Using phenomenological analysis, we demonstrated that the failure of these attempts and the existence of imbroglio itself are most likely due to the misunderstanding of the physical meaning of temperature and to some serious flaws in foundations of classical thermodynamics. We have finally shown that the temperature of a moving body must remain invariant for observers in all relatively moving frames.
We also took advantage of our extensive knowledge of electric charge transport in conductors in order to shad a new light on the electric signal transfer through nerve fibre. The governing standard theory as established by Hodgkin and Huxley in the 1950’s, uses for the description of action potential a clever combination of various concepts of electrochemistry and circuit theory; however, this theory neglects some fundamental features of charge transport through any conductor, e.g. the temporal existence of a sphondyloid structure accompanied by an external electric field. The consequences of this fact are, among others, the introduction of a non-adequate concept of “conduction velocity” and the obscure idea of saltatory propagation of action potential in myelinated nerve fibres. Our approach, based on standard transport theory and, particularly, on the submarine cable model, describes the movement of the front of the action potential as a diffusion process characterized by the diffusion constant DE. This process is physically realized by the redistribution of ions in the nervous fluid (axoplasm), which is controlled by another diffusion constant DQ << DE. Since the action bound with the movement of Na+ and K+ cations prevailing in the axoplasm is comparable with the Planck constant ħ, the signal transfer is actually a quantum process. This fact accounts for the astonishing universality of the transfer of action potential, which is proper to quite different species of animals. As is further shown, the observed diversity in the behaviour of nerve tissues is controlled by the scaling factor (DQ /DE)½, where DQ is of a quantum nature and DE of an essentially geometric one.
