  We present the linear response matrix for a sliding domain wall in a
rotatable magnetic nanowire, which is driven out of equilibrium by temperature
and voltage bias, mechanical torque, and magnetic field. An expression for
heat-current induced domain wall motion is derived. Application of Onsager's
reciprocity relation leads to a unified description of the Barnett and
Einstein-de Haas effects as well as spin-dependent thermoelectric properties.
We envisage various heat pumps and engines, such as coolers driven by magnetic
fields or mechanical rotation as well as nanoscale motors that convert
temperature gradients into useful work. All parameters (with the exception of
mechanical friction) can be computed microscopically by the scattering theory
of transport.
