  The concept of temperature in nonequilibrium thermodynamics is an outstanding
theoretical issue. We propose an energy repartition principle that leads to a
spectral (mode-dependent) temperature in steady-state nonequilibrium systems.
The general concepts are illustrated by analytic solutions of the classical
Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary
temperature profiles. Gradients of external magnetic fields are shown to
localize spin waves in a Wannier-Zeemann fashion, while magnon interactions
renormalize the spectral temperature. Our generic results are applicable to
other thermodynamic systems such as Newtonian liquids, elastic solids, and
Josephson junctions.
