Thermal angular Doppler effect , polarized thermal waves and thermal rotational superradiance

We discuss at first the old question, studied originally by Planck and Einstein, whether thermodynamic equilibrium could be described by a covariant law or if it was an invariant property in every reference frame. In particular we analyze briefly the historical debate, which this problem stimulated, about the correct transformation law of the equilibrium temperature of a moving body. We outline its relevance for possible generalization of the Stefan-Boltzman radiative law for spinning macroscopic sources, suggesting a possible coupling between thermal radiative and conductive processes in a rotating conductor heated by a laser source. We analyze then the problem of the Doppler effect of a thermal wave propagating in a rotating frame, with a constant angular velocity. We extend the approach based on the Wilson equation, used recently [1], to deduce a translational Doppler effect, showing the existence of a frequency shift that we call rotational thermal Doppler effect. We predict, under a particular condition, a thermal wave with negative frequency which, we interpret, as a thermal analogue of the rotational superradiance effect discovered fifty years ago by Zel’dovich [2]. We show, assuming a more general approach based on the non homogeneous telegraphist equation, that exist particular surface thermal waves with negative frequency which transport angular momentum. We interpret this heat wave diffusion process as a cooling effect due to microscopic Coriolis forces. These inertial forces cause thermal waves to propagate helicoidally, in a very similar way to what discovered recently on spin-polarized acoustic waves [3] and on acoustic rotational superradiance [4]. We remark finally the possible relevance for future applications to unidirectional heat control of the spin polarized helicoidal thermal waves illustrated in this talk.