Cooling of mechanical vibrations by heat flow

We theoretically consider a nanomechanical link between two metallic leads subject to a temperature drop. It is shown that mechanical dynamics of such system can be strongly affected by a heat flow through it via the position dependent electron-electron interaction, even though the electronic transport between leads is blocked. In particular, it is demonstrated that, under certain conditions, the stationary distribution of the excitations in the mechanical subsystem has a Boltzmann form with an effective temperature, which is much lower than the temperature of the environment; this seems rather counterintuitive. We also find that a change in the direction of the temperature gradient can result in the generation of mechanical vibrations rather than the heating of the mechanical subsystem.