  We present a model independent, operator algebraic approach to
non-equilibrium quantum thermodynamics within the framework of two-dimensional
Conformal Field Theory. Two infinite reservoirs in equilibrium at their own
temperatures and chemical potentials are put in contact through a defect line,
possibly by inserting a probe. As time evolves, the composite system then
approaches a non-equilibrium steady state that we describe. In particular, we
re-obtain recent formulas of Bernard and Doyon.
