  In this work, we show that the quantum coherence among non-degenerate energy
subspaces (CANES) is essential for the energy flow in any quantum system. CANES
satisfies almost all of the requirements as a coherence measure, except that
the coherence within degenerate subspaces is explicitly eliminated.We show that
the energy of a system becomes frozen if and only if the corresponding CANES
vanishes, which is true regardless of the form of interaction with the
environment. However, CANES can remain zero even if the entanglement changes
over time. Furthermore, we show how the power of energy flow is bounded by the
value of CANES. An explicit relation connecting the variation of energy and
CANES is also presented. These results allow us to bound the generation of
system-environment correlation through the local measurement of the system's
energy flow.
