On Fröhlich's coherent effects in biological systems: influence of carriers and high order dissipative effects

Following Fröhlich we consider a system that models a biological one, for example, a long chain of proteins possessing polar modes of vibration and where energy is pumped through metabolic processes. We consider the effect produced by free electrons that are usually present as hole carriers in proteins with electron-donor molecules. A theory of relaxation based on the non-equilibrium statistical operator method is used in the derivation of the kinetic equations to introduce non-linearities due to interactions of the polar vibrations with the carriers and with a thermal bath. These non-linearities arising from high order relaxation processes lead to the emergence of the Fröhlich effect in the polar modes, i.e. the occurrence of a (non-equilibrium) Bose-Einstein-like condensation. It points to an instability of the system that seems to be followed by a morphological transformation in the form of a spatially ordered dissipative structure.