  We consider the large deviations from the hydrodynamic limit of the Totally
Asymmetric Simple Exclusion Process (TASEP). This problem was studied in Jensen
(2000) and Varadhan (2004) and was shown to be related to entropy production in
the inviscid Burgers equation. Here we prove the full large deviation
principle. Our method relies on the explicit formula of Matetski, Quastel, and
Remenik (2016) for the transition probabilities of the TASEP.
