  In Markovian dynamics with the local detailed balance condition, we decompose
the total entropy production rate into microscopic transitions. By applying
this decomposition to the heat to work conversion process, we rigorously show
that the Carnot efficiency implies zero power for any heat engine, even with
broken time-reversal symmetry beyond the linear response regime. Moreover, we
propose a trade-off relationship between the entropy production rate and the
heat flow between the system and bath.
