  A generally relativistic theory of thermodynamics is developed, based on four
main physical principles: heat is a local form of energy, therefore described
by a thermal energy tensor; conservation of mass, equivalent to conservation of
heat, or the local first law; entropy is a local current; and non-destruction
of entropy, or the local second law. A fluid is defined by the thermostatic
energy tensor being isotropic. The entropy current is related to the other
fields by certain equations, including a generalised Gibbs equation for the
thermostatic entropy, followed by linear and quadratic terms in the dissipative
(thermal minus thermostatic) energy tensor. Then the second law suggests
certain equations for the dissipative energy tensor, generalising the Israel-
Stewart dissipative relations, which describe heat conduction and viscosity
including relativistic effects and relaxation effects. In the thermostatic
case, the perfect-fluid model is recovered. In the linear approximation for
entropy, the Eckart theory is recovered. In the quadratic approximation for
entropy, the theory is similar to that of Israel & Stewart, but involving
neither state-space differentials, nor a non-equilibrium Gibbs equation, nor
non-material frames. Also, unlike conventional thermodynamics, the thermal
energy density is not assumed to be purely thermostatic, though this is derived
in the linear approximation. Otherwise, the theory reduces in the non-
relativistic limit to the extended thermodynamics of irreversible processes due
to Mueller. The dissipative energy density seems to be a new thermodynamical
field, but also exists in relativistic kinetic theory of gases.
