  The analytically tractable model employing Quantum Markovian Master
Equations, derived by weak coupling procedure and satisfying complete
positivity, is proposed to describe a model of molecular battery charged by a
non-equilibrium excitonic reservoir. The excitons are produced by
non-equilibrium processes involving, e.g. light absorption and chemical
reactions. Various relations concerning the efficiency of the involved
processes of energy transfer and the stability of battery are discussed. The
model can be treated as an initial step in applications of mathematically sound
version of Quantum Theory of Open Systems to complex processes of energy
transfer in biological system and man-made devices based on organic materials.
