  In this paper we demonstrate that Lindblad equations characterized by a
random rate variable arise after tracing out a complex structured reservoir.
Our results follows from a generalization of the Born-Markov approximation,
which relies in the possibility of splitting the complex environment in a
direct sum of sub-reservoirs, each one being able to induce by itself a
Markovian system evolution. Strong non-Markovian effects, which microscopically
originate from the entanglement with the different sub-reservoirs, characterize
the average system decay dynamics. As an example, we study the anomalous
irreversible behavior of a quantum tunneling system described in an effective
two level approximation. Stretched exponential and power law decay behaviors
arise from the interplay between the dissipative and unitary hopping dynamics.
