  The striking efficiency of energy transfer in natural photosynthetic systems
and the recent evidence of long-lived quantum coherence in biological light
harvesting complexes has triggered much excitement, due to the evocative
possibility that these systems - essential to practically all life on earth --
use quantum mechanical effects to achieve optimal functionality. A large body
of theoretical work has addressed the role of local environments in determining
the transport properties of excitons in photosynthetic networks and the
survival of quantum coherence in a classical environment. Nonetheless,
understanding the connection between quantum coherence, exciton network
geometry and energy transfer efficiency remains a challenge. Here we address
this connection from the perspective of heat transfer within the exciton
network. Using a non-equilibrium open quantum system approach and focusing on
the Fenna-Matthews-Olson complex, we demonstrate that finite local dephasing
can be beneficial to the overall power output. The mechanism for this
enhancement of power output is identified as a gentle balance between quantum
and classical contributions to the local heat flow, such that the total heat
flow is directed along the shortest paths and dissipation is minimized.
Strongly related to the spatial network structure of the exciton transfer
complex, this mechanism elucidates how energy flows in photosyntetic excitonic
complexes.
