  We review product form blocking measures in the general framework of nearest
neighbor asymmetric one dimensional misanthrope processes. This class includes
exclusion, zero range, bricklayers, and many other models. We characterize the
cases when such measures exist in infinite volume, and when finite boundaries
need to be added. By looking at inter-particle distances, we extend the
construction to some 0-1 valued particle systems e.g., q-ASEP and the
Katz-Lebowitz-Spohn process, even outside the misanthrope class. Along the way
we provide a full ergodic decomposition of the product blocking measure into
components that are characterized by a non-trivial conserved quantity.
Substituting in simple exclusion and zero range has an interesting consequence:
a purely probabilistic proof of the Jacobi triple product, a famous identity
that mostly occurs in number theory and the combinatorics of partitions.
Surprisingly, here it follows very naturally from the exclusion - zero range
correspondence.
