  Considering the standard abelian sandpile model in one dimension, we
construct an infinite volume Markov process corresponding to its thermodynamic
(infinite volume) limit. The main difficulty we overcome is the strong
non-locality of the dynamics. However, using similar ideas as in recent
extensions of the standard Gibbs formalism for lattice spin systems, we can
identify a set of `good' configurations on which the dynamics is effectively
local. We prove that every configuration converges in a finite time to the
unique invariant measure.
