  It is shown that the timelike asymptotic properties of thermal correlation
functions in relativistic quantum field theory can consistently be described in
terms of free fields carrying some stochastic degree of freedom which couples
to the thermal background. These ``asymptotic thermal fields'' have specific
algebraic properties (commutation relations) and their dynamics can be
expressed in terms of asymptotic field equations. The formalism is applied to
interacting theories where it yields concrete non-perturbative results for the
asymptotic thermal propagators. The results are consistent with the expected
features of dissipative propagation of the constitutents of thermal states,
outlined in previous work, and they shed new light on the non-perturbative
effects of thermal backgrounds.
