  We study the coupled particle and energy transport in a prototype model of
interacting one-dimensional system: the disordered hard-point gas, for which
numerical data suggest that the thermoelectric figure of merit ZT diverges with
the system size. This result is explained in terms of a microscopic mechanism,
namely the local equilibrium is characterized by the emergence of a broad
stationary "modified Maxwell-Boltzmann velocity distribution", of width much
larger than the mean velocity of the particle flow.
