Most of the evolution of the universe takes place in thermal equilibrium, i.e. its dynamics is reversible. This can be directly deduced from the Friedmann equations, which are invariant under time inversion. Nevertheless, during some events the universe is certainly out of equilibrium and, thus, its evolution becomes irreversible. Such irreversibility can be incorporated into General relativity by means of a covariant variational description. When applied to cosmology, this delivers a modification of the second Friedmann equations that predicts an acceleration of the expansion during periods of entropy production. In light of this, we investigate how the growth of entropy of the causal horizon in an open inflation scenario may explain the current accelerated expansion of the universe without the need of a cosmological constant.