  Heat transport has large potentialities to unveil new physics in mesoscopic
systems. A striking illustration is the integer quantum Hall regime, where the
robustness of Hall currents limits information accessible from charge
transport. Consequently, the gapless edge excitations are incompletely
understood. The effective edge states theory describes them as prototypal
one-dimensional chiral fermions - a simple picture that explains a large body
of observations and calls for quantum information experiments with quantum
point contacts in the role of beam splitters. However, it is in ostensible
disagreement with the prevailing theoretical framework that predicts, in most
situations, additional gapless edge modes. Here, we present a setup which gives
access to the energy distribution, and consequently to the energy current, in
an edge channel brought out-of-equilibrium. This provides a stringent test of
whether the additional states capture part of the injected energy. Our results
show it is not the case and thereby demonstrate regarding energy transport, the
quantum optics analogy of quantum point contacts and beam splitters. Beyond the
quantum Hall regime, this novel spectroscopy technique opens a new window for
heat transport and out-of-equilibrium experiments.
