The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid

TLDR

The first paper’s considerations are modified to align with special relativity, and matter is interpreted as the number of molecules rather than inertia. Its velocity vector defines local proper‑time axes, and the energy‑momentum tensor is resolved into proper‑time and space components. The study shows that the inertia of energy does not eliminate the need for matter conservation, the first law of thermodynamics is a scalar, temperature and entropy are scalars, and relativistic generalizations of Fourier’s law, viscosity, and Ohm’s law follow from the second law.

Abstract

The considerations of the first paper of this series are modified so as to be consistent with the special theory of relativity. It is shown that the inertia of energy does not obviate the necessity for assuming the conservation of matter. Matter is to be interpreted as number of molecules, therefore, and not as inertia. Its velocity vector serves to define local proper-time axes, and the energy momentum tensor is resolved into proper-time and -space components. It is shown that the first law of thermodynamics is a scalar equation, and not the fourth component of the energy-momentum principle. Temperature and entropy also prove to be scalars. Simple relativistic generalizations of Fourier's law of heat conduction, and of the laws of viscosity are obtained from the requirements of the second law. The same considerations lead directly to the accepted relativistic form of Ohm's law.