Covariant formulation of nonequilibrium thermodynamics in General Relativity
Abstract
We construct a generallycovariant formulation of nonequilibrium thermodynamics in General Relativity. We find covariant entropic forces arising from gradients of the entropy density, and a corresponding nonconservation of the energy momentum tensor in terms of these forces. We also provide a Hamiltonian formulation of General Relativity in the context of nonequilibrium phenomena and write the Raychaudhuri equations for a congruence of geodesics. We find that a fluid satisfying the strong energy condition could avoid collapse for a positive and sufficiently large entropicforce contribution. We then study the forces arising from the internal production of "bulk" entropy of hydrodynamical matter, as well as from the entropy gradients in the boundary terms of the action, like those associated with black hole horizons. Finally, we apply the covariant formulation of nonequilibrium thermodynamics to the expanding universe and obtain the modified Friedmann equations, with an extra term corresponding to an entropic force satisfying the second law of thermodynamics.
 Publication:

Physics of the Dark Universe
 Pub Date:
 December 2021
 DOI:
 10.1016/j.dark.2021.100893
 arXiv:
 arXiv:2106.16012
 Bibcode:
 2021PDU....3400893E
 Keywords:

 General relativity;
 Nonequilibrium Thermodynamics;
 Dark energy;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 14 pages. Comments and references added. New section dealing with real fluids added. Matches accepted version by PDU