  When driven by a potential bias between two finite reservoirs, the particle
current across a quantum system evolves from an initial loading through a
coherent, followed by a metastable phase, and ultimately fades away upon
equilibration. We formulate a theory which fully accounts for the associated,
distinct time scales, and identifies the parameter dependence of the decay rate
which ultimately controls the convergence towards equilibrium. Our formalism
guarantees total particle number conservation and fundamental consistency
between macroscopic and internal currents flowing in the system. We furthermore
establish a clear imprint of the fermionic or bosonic particle character on the
resulting conductance.
