  We consider two qubits interacting with local and collective thermal
reservoirs. Each spin-reservoir interaction consists of an energy exchange and
an energy conserving channel. We prove a resonance representation of the
reduced dynamics of the spins, valid for all times t>=0, with errors (small
interaction) estimated rigorously, uniformly in time. Subspaces associated to
non-interacting energy differences evolve independently, partitioning the
reduced density matrix into dynamically decoupled clusters of jointly evolving
matrix elements. Within each subspace the dynamics is markovian with a
generator determined entirely by the resonance data of the full Hamiltonian.
Based on the resonance representation we examine the evolution of entanglement
(concurrence). We show that, whenever thermalization takes place, entanglement
of any initial state dies out in a finite time and will not return. For a
concrete class of initially entangled spin states we find explicit bounds on
entanglement survival and death times in terms of the initial state and the
resonance data.
