Role of nonequilibrium entropy in Einstein’s theory of gravitation

We employ the covariant version of a systematic framework of nonequilibrium thermodynamics to clarify the role of entropy in the classical theory of gravitation. An expression for the global entropy is identified naturally from the covariant formulation, and a dual role of the Einstein equation as a fundamental evolution equation and as a thermodynamic equation of state follows immediately. The covariant time integral of the entropy is a more fundamental quantity than the entropy itself. In the absence of matter, the gravitational entropy alone cannot generate any irreversible processes. Some implications for the structure of a quantum theory of gravity are discussed.