  In this paper, we establish uniqueness of the solution of the Vlasov-Poisson
system with spatial density belonging to a certain class of Orlicz spaces. This
extends the uniqueness result of Loeper (which holds for uniformly bounded
density) and the uniqueness result of the second author. Uniqueness is a direct
consequence of our main result, which provides a quantitative stability
estimate for the Wasserstein distance between two weak solutions with spatial
density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability
for mean-field PDEs. Our proofs are built on the second-order structure of the
underlying characteristic system associated to the equation.
