Hyperbolic heat equation in Kaluza's magnetohydrodynamics

TL;DR

This paper derives a hyperbolic heat conduction equation within Kaluza's five-dimensional framework, showing it respects thermodynamics and predicts a finite propagation speed slightly below light speed, with potential astrophysical implications.

Contribution

It introduces a hyperbolic heat equation in Kaluza's magnetohydrodynamics, linking thermodynamics with higher-dimensional gravity theories.

Findings

Heat propagation speed is slightly below light speed.

The equation aligns with the second law of thermodynamics.

Potential applications in galaxy cluster physics.

Abstract

This paper shows that a hyperbolic equation for heat conduction can be obtained directly using the tenets of linear irreversible thermodynamics in the context of the five dimensional space-time metric originally proposed by T. Kaluza back in 1922. The associated speed of propagation is slightly lower than the speed of light by a factor inversely proportional to the specific charge of the fluid element. Moreover, consistency with the second law of thermodynamics is achieved. Possible implications in the context of physics of clusters of galaxies of this result are briefly discussed.