  The heat flow between a quantum system and its reservoir is analyzed when
initially both are in a separable thermal state and asymptotically approach a
correlated equilibrium. General findings are illustrated for specific systems
and various classes of non-Markovian reservoirs. System-bath correlations are
shown to be substantial at low temperatures even in the weak coupling regime.
As a consequence, predictions of work and heat for actual experiments obtained
within conventional perturbative approaches may often be questionable.
Correlations induce characteristic imprints in heat capacities which opens a
proposal to measure them in solid state devices.
