Long-range resonant interactions in biological systems

TL;DR

This paper revisits classical electrodynamics to analyze long-range resonant interactions between molecules, revealing that such interactions are significant only out of thermal equilibrium, with implications for biophysical theories.

Contribution

It introduces a simple complex analysis method to determine normal mode frequencies and estimates interaction potentials, aligning with quantum results and challenging previous beliefs.

Findings

Resonant interactions are significant only out of thermal equilibrium.

The method aligns classical and quantum results for interaction potentials.

Challenges the belief that long-range interactions occur at thermal equilibrium.

Abstract

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to work out the frequencies of the normal modes, which are then used to estimate the interaction potential. The main results thus found are in perfect agreement with several outcomes obtained from quantum computations. Moreover, when applied to a biophysical context, our findings shed new light on Fr\"ohlich's theory of selective long-range interactions between biomolecules. In particular, at variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.