On the Interpretation of Heat in Relativistic Thermodynamics

This article investigates the interpretation of the right-hand side of the relativistic second law of thermodynamics ${\left({\phi }_0\frac{d{x}^{\mu }}{\mathrm{ds}}\right)}_{\mu }{\mathrm{}(-g)\mathrm{}}^{\frac{1}{2}}d{x}^{1}d{x}^{2}d{x}^{3}d{x}^4\geqq \frac{d{Q}_0}{T_0}$ and shows that the quantity $d{Q}_0$ can be interpreted as the heat—measured by a local observer at rest in the fluid at the point of interest—which flows relative to the fluid into an element of the fluid having the instantaneous proper volume $d{V}_0$ during the proper time $d{t}_0$, where these quantities are chosen so as to satisfy the numerical equality $d{V}_{0}d{t}_0={\mathrm{}(-g)\mathrm{}}^{\frac{1}{2}}d{x}^{1}d{x}^{2}d{x}^{3}d{x}^4$ and the quantity $T_0$ is taken as the temperature ascribed to this heat by the local observer.