We present a generalized relativistic Lagrangian which yields the effect of heat flux q and nonequilibrium stress τ in the energy-momentum tensor of an extended reversible fluid exhibiting thermal inertia. The actual momentum of heat (thermal momentum related to the entropy flow) follows to be many orders of magnitude larger than $\mathbf{q}{/c}^2$ (c is the light speed) but it is consistent with Grad’s kinetic theory [in Principles of the Theory of Gases, edited by S. Flugge, Handbüch der Physik Vol. 12 (Springer, Berlin, 1958)] and with experiments in heat conduction. On the other hand, the net momentum of heat remains $\mathbf{q}{/c}^2,$ in agreement with the standard relativistic result, this net momentum being the result of incomplete compensation of the actual thermal momentum and the momentum associated with self-diffusion of particles. The classical densities of mass and entropy, ρ and ${\rho }_s,$ cease to be natural variables of energy density E in the sense of Callen [Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1988)] whenever inertial effects prevail. This fact necessitates the use of what may be called the thermal potential $T^{-},$ a new quantity replacing the classical temperature T. Changes in thermodynamic formalism are related to the replacement of T by $T^{-}.$ The admission of a freely varied four-flux of entropy in an extended Hamilton principle implies all nonequilibrium corrections (q and τ) to the energy-momentum tensor, making it possible to investigate the effect of nonequilibrium phenomena on the properties of associated gravitational fields.

• Received 9 February 1998

DOI:https://doi.org/10.1103/PhysRevE.58.7027