  We consider a situation where an $N$-level system (NLS) is coupled
successively to two heat baths with different temperatures without being
necessarily thermalized and approaches a steady state. For this situation we
apply a general Jarzinski-type equation and conclude that heat and entropy is
flowing from the hot bath to the cold one. The Clausius relation between
increase of entropy and transfer of heat divided by a suitable temperature
assumes the form of two inequalities. Our approach is illustrated by an
analytical example. For the linear regime, i.~e., for small temperature
differences between the two heat baths we derive an expression for the heat
conduction coefficient.
