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In this article, we explore the dynamical decoherence of the chromophoreswithin a green fluorescent protein when coupled to a finite-temperaturedielectric environment. Such systems are of significant interest due to theiranomalously long coherence lifetimes compared to other biomolecules. We workwithin the spin-boson model and employ the Hierarchical Equations of Motionformalism which allows for the accounting of the full non-perturbative andnon-Markovian characteristics of the system dynamics. We analyse the levelcoherence of independent green fluorescent protein chromophores and the energytransfer dynamics in homo-dimer green fluorescent proteins, focusing on theeffect of dielectric relaxation on the timescales of these systems. Using theFluctuation-Dissipation theorem, we generate spectral densities from localelectric susceptibility generated from Poisson's equation and employ a Debyedielectric model for the solvent environment. For different systemarchitectures, we identify a number of very striking features in the dynamicsof the chromophore induced by the dielectric relaxation of the environment,resulting in strong memory effects that extend the coherence lifetime of thesystem. Remarkably, the complex architecture of the green fluorescent protein,which includes a cavity-like structure around the atomic system, is well suitedto preserving the coherences in the homo-dimer system. The system dynamicsgenerate a dynamical correlation between the coherent energy transfer betweenits sub-systems and the entropy production, which can lead to transientreductions in entropy, a unique feature of the non-Markovian nature of thesystem-environment interaction.

Dynamical Decoherence and Memory Effects in Green Fluorescent Proteins by Dielectric Relaxation