A possible dynamical phase transition between the dissipative and the non-dissipative solutions of a thermal process

Previously, we have introduced an abstract scalar field to generate a dynamical temperature and a covariant field equation to describe the heat propagation with finite speed—less than the speed of light—of action. Moreover, we have showed how this scalar field can be connected to the usual temperature (local equilibrium temperature) and the Fourier's heat conduction. In present Letter we make an attempt to point out that there is a dynamical phase transition between these two kinds of propagation, between a wave and a non-wave, or with an other context it is better to say, a dynamical phase transition between a non-dissipative and a dissipative thermal process.