  We investigate whether the dynamical lattice supersymmetry discussed for
various Hamiltonians, including one-dimensional quantum spin chains, by Fendley
et.al. and Hagendorf et.al. might also exist for the Markov matrices of any
one-dimensional exclusion processes, since these can be related by conjugation
to quantum spin chain Hamiltonians. We find that the DiSSEP (Dissipative
Symmetric Simple Exclusion Process), introduced by Crampe et.al. provides one
such example for suitably chosen parameters. The DiSSEP Markov matrix admits
the supersymmetry in these cases because it is conjugate to spin chain
Hamiltonians which also possess the supersymmetry. We note that the
length-changing supersymmetry relation for the DiSSEP Markov matrix and the
supercharge is reminiscent of a "transfer matrix" symmetry that has been
observed in other exclusion processes and discuss the similarity.
