Entropy and irreversible processes in gravity and cosmology

General Relativity is a priori a theory invariant under time reversal. Its integration with the laws of thermodynamics allows for a formulation of non-equilibrium phenomena in gravity and the introduction of an arrow of time, i.e. the the breaking of such invariance. Even though most of the evolution of the universe takes place in local thermal equilibrium, the effects of irreversible processes on the expansion via entropic forces may be phenomenologically relevant. We review our previous work on the covariant formulation of non-equilibrium thermodynamics in General Relativity and the proposal to explain the recent cosmic acceleration from it.