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We assume an open system is coupled to a second quantum system, bath B. However, this is not the whole story as under actual physical conditions, the bath is also coupled to the rest of the world, not accounted for in defining B. Such a secondary environmental influence manifests itself in the choice of bath initial state or bath fluctuation characteristics. 762mm CUUK2541/Mohseni et al. 198mm 978 1 107 01080 2 December 20, 2013 Open quantum system approaches to biological systems Taking a trace of this over the bath and using the fact that P ρI (t) = ρS,I (t) ⊗ ρB (0), we find that d ρS,I (t) dt = − iTrB [LSB,I (t)ρB (0)]ρS,I (t) ˆ t − iTrB [LSB,I (t)T+ exp −i dτ QLSB,I (τ ) QρI (0)] ˆ − 0 t ˆ dτ TrB [LSB,I (t)T+ exp −i 0 t dτ QLSB,I (τ ) QLSB,I (τ )ρB (0)]ρS,I (τ ).

A biology related example is the case of the light absorption process by electronic state of a molecule, where the applicability of the Franck–Condon condition can distinguish a CP from a non-CP dynamical process of electronic states. The Franck– Condon principle states that the internal dynamics of electronic states can happen over much faster timescales than the dynamics of nuclear states, such that nuclear DOF can be considered to be dynamically frozen (Atkins and Friedman, 1999) during the light absorption process.

This explain why any non-SL state can be well approximated by a SL state. The dynamics for a non-SL state is also described by a map. 5), we find, † ρS (t) = αij TrB [USB (t)|i j | ⊗ ϕij USB (t)] ij(SL) † + βij TrB [USB (t)|i j | ⊗ ψij USB (t)]. 11) has no contribution to the system, only state ρS = TrB [ρSB ], thus can be treated as a constant Knon−SL . 198mm CUUK2541/Mohseni et al. 9). It is argued in Shabani and Lidar (2009a) that the above affine map is actually linear, considering the map acting only on the space of the density matrices.