  We show that the recently discovered universal upper bound on the thermal
conductance of a single channel comprising particles obeying arbitrary
fractional statistics is in fact a consequence of a more general universal
upper bound, involving the averaged entropy and energy currents of a single
channel connecting heat reservoirs with arbitrary temperatures and chemical
potentials. The latter upper bound in turn leads, via Holevo's theorem, to a
universal (i.e., statistics independent) upper bound on the optimum capacity
for classical information transmission down a single, wideband quantum channel.
