  The existence of long-lived non-equilibrium states without showing
thermalization, which has previously been demonstrated in time evolution of
ultracold atoms, suggests the possibility of their spatial analogue in
transport behavior of interacting electrons in solid-state systems. Here we
report long-lived non-equilibrium states in one-dimensional edge channels in
the integer quantum Hall regime. An indirect heating scheme in a
counterpropagating configuration is employed to generate a non-trivial binary
spectrum consisting of high- and low-temperature components. This unusual
spectrum is sustained even after travelling 5 - 10 {\mu}m, much longer than the
length for electronic relaxation (about 0.1 {\mu}m), without showing
significant thermalization. This observation is consistent with the integrable
model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the
system is well described by non-interacting plasmons, which are attractive for
carrying information for a long distance.
