Covariant formulation of non-equilibrium thermodynamics in General Relativity

TL;DR

This paper develops a covariant framework for non-equilibrium thermodynamics in General Relativity, linking entropy gradients to forces and modifying Einstein's equations to include entropic effects, with applications to cosmology.

Contribution

It introduces a covariant, Hamiltonian-based formulation of non-equilibrium thermodynamics in General Relativity, incorporating entropic forces into gravitational dynamics.

Findings

Covariant entropic forces arise from entropy density gradients.

A fluid with strong energy condition can avoid collapse due to entropic forces.

Modified Friedmann equations include an entropic force term.

Abstract

We construct a generally-covariant formulation of non-equilibrium thermodynamics in General Relativity. We find covariant entropic forces arising from gradients of the entropy density, and a corresponding non-conservation of the energy momentum tensor in terms of these forces. We also provide a Hamiltonian formulation of General Relativity in the context of non-equilibrium 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 entropic-force contribution. We then study the forces arising from gradients of the bulk entropy of hydrodynamical matter, as well as the entropy of boundary terms in the action, like those of black hole horizons. Finally, we apply the covariant formulation of non-equilibrium 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.