Abstract
In this article, we explore the dynamical decoherence of the chromophores
within a green fluorescent protein when coupled to a finite-temperature
dielectric environment. Such systems are of significant interest due to their
anomalously long coherence lifetimes compared to other biomolecules. We work
within the spin-boson model and employ the Hierarchical Equations of Motion
formalism which allows for the accounting of the full non-perturbative and
non-Markovian characteristics of the system dynamics. We analyse the level
coherence of independent green fluorescent protein chromophores and the energy
transfer dynamics in homo-dimer green fluorescent proteins, focusing on the
effect of dielectric relaxation on the timescales of these systems. Using the
Fluctuation-Dissipation theorem, we generate spectral densities from local
electric susceptibility generated from Poisson's equation and employ a Debye
dielectric model for the solvent environment. For different system
architectures, we identify a number of very striking features in the dynamics
of the chromophore induced by the dielectric relaxation of the environment,
resulting in strong memory effects that extend the coherence lifetime of the
system. Remarkably, the complex architecture of the green fluorescent protein,
which includes a cavity-like structure around the atomic system, is well suited
to preserving the coherences in the homo-dimer system. The system dynamics
generate a dynamical correlation between the coherent energy transfer between
its sub-systems and the entropy production, which can lead to transient
reductions in entropy, a unique feature of the non-Markovian nature of the
system-environment interaction.