  By revisiting previous definitions of the heat current operator, we show that
one can define a heat current operator that satisfies the continuity equation
for a general Hamiltonian in one dimension. This expression is useful for
studying electronic, phononic and photonic energy flow in linear systems and in
hybrid structures. The definition allows us to deduce the necessary conditions
that result in current conservation for general-statistics systems. The
discrete form of the Fourier's Law of heat conduction naturally emerges in the
present definition.
