Heat conduction and relaxation in liquids of high viscosity

The generalized hydrodynamic description of heat conduction in liquids of high viscosity is presented, following the phenomenological theory of thermoviscoelasticity. The theory applies in particular to undercooled one-component liquids near the glass transition, in which structural relaxation causes the specific heat to be frequency dependent. For a simple model in which a separate channel for the flow of configurational energy independent of phonons exists, it is shown that a frequency dependence of the thermal conductivity goes together with a wavevector dependence of the specific heat. The spectrum of the thermal entropy fluctuations and the quasi-elastic light scattering spectrum, which display the interference of the heat conduction mode with structural relaxation, are derived from the phenomenological equations.