Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review

We review a theoretical and experimental programme addressing two closely related phenomena in biophysics: the classical analogue of Fröhlich phonon condensation in macromolecules driven out of thermal equilibrium, and the resulting activation of long-range resonant electrodynamic intermolecular this http URL first is obtained by applying the time-dependent variational principle (TDVP) to the quantum Wu-Austin model,yielding a fully classical Hamiltonian in action-angle variables whose nonlinear rate equations display a nonequilibrium phase transition: supplied energy is channelled into the lowest-frequency collective mode.

The second is based on a classical electrodynamic Hamiltonian for two coupled oscillating dipoles, whose normal modes predict long-range (1/r^3) resonant interactions.

These are absent at thermal equilibrium but emerge under out-of-equilibrium coherent this http URL also discuss how to link Fröhlich rate equations directly to Hamilton equations, clarifying the role of bath-mediated nonlinear couplings and the conditions for strong condensation at room this http URL addition, TDVP is applied to a Davydov-Holstein-Fröhlich model describing electron-phonon dynamics along a specific DNA sequence and its cognate restriction enzyme EcoRI.

The time-domain Fourier cross-spectrum of the resulting electron currents shows a sharp co-resonance peak for the canonical recognition sequence, which disappears under randomisation, providing a sequence-specific electrodynamic signature of DNA-protein this http URL evidence from THz near-field spectroscopy, fluorescence correlation spectroscopy, and direct protein clustering is reviewed.

Together these results support the view that metabolic energy can drive macromolecules into coherent oscillatory states, activating selective long-range electrodynamic forces relevant to biochemical organisation in living matter.