Theorems on Amplification of Fluctuations and their Biological Implications

Abstract

Three theorems on amplification of fluctuations at nonequilibrium are proposed: (1) Amplification of a fluctuation is possible within a closed system. (2) The second-order time derivative of Boltzmann's H-quantity may contain terms of negative value. (3) An H-theorem for open systems. It is pointed out in the paper that the fact that microscopic transition rates are not all identical constitutes the basis of the theorems proposed. And this nonidenticalness is also a fundamental reason why phenomena defying the thermodynamic law in an apparent way (such as life) exist in the course of evolution. It is also pointed out in the paper that at states far from thermal equilibrium it is “selection” instead of “averaging” that works in the statistics of the quantum states. Finally it is speculated that certain key biomolecules such as ATP are situated at long lifetime excited states, thus at states far from thermal equilibrium. The biomolecules are large fluctuations produced or amplified during a relaxation process starting from an extreme initial state (even further from equilibrium), and stabilized by solar radiation in the present day. Again, selection takes the place of an averaging which is artificial and which Ievels out the whole set of transition rates.

A Statistical Physical Interpretation for the Thermodynamic Formulation $\frac{dS}{dt} = \frac{d_{i}S}{dt} + \frac{d_{e}S}{dt}$

“…[5]) a pumping mechanism was introduced by the author and consequently the conditions for entropy decrease were obtained. I have been aware of the fact that the pumping must take a mechanism different from that of the direct relaxation, as this thought was once revealed in the article of mixed particles and photons 1 . Now the time has come for a deeper analysis to be made as the consequence of a maturing thought.…”

“…In two previous papers (Ref. [1] and Ref. [5]) a pumping mechanism was introduced by the author and consequently the conditions for entropy decrease were obtained.…”