On the theory of nonlinear thermal conductivity

A nonlinear differential equation of thermal conductivity is derived phenomenologically from the general principles of construction of functional Q invariant to the inversion operation $I(\mathbf{r}\to -\mathbf{r})$, and the temperature evolution dynamics is analyzed in the nonstationary case. The proposed method makes it possible to reveal some general regularities in the physical behavior of such systems for describing irreversible phenomena in self-organization processes. It is noted that an analogous situation may take place, for example, in strongly inhomogeneous structures with stochastic internal heat fluxes.