Relativistic heat conduction.

*(English)*Zbl 1189.80009Summary: The hyperbolic heat conduction equation (HHCE), which acknowledges the finite speed of heat propagation, is based on microscopic evidence from the kinetic theory and statistical mechanics. However, it was argued that the HHCE could violate the second law of thermodynamics. This paper shows that a HHCE-like equation (RHCE) can be derived directly from the theory of relativity, as a direct consequence of space-time duality, without any consideration of the microstructure of the heat-conducting medium. This approach results in an alternative expression for the heat flux vector that is more compatible with the second law. Therefore, the RHCE brings the classical field theory of heat conduction into agreement with other branches of modern physics.

##### MSC:

80A20 | Heat and mass transfer, heat flow (MSC2010) |

83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |