  If $L$ is a relational language, then an $L$-structure ${\mathbb X}=\langle
X,\bar \rho \rangle$ is reversible iff there is no interpretation $\bar \sigma
\varsubsetneq \bar \rho$ such that the structures $\langle X,\bar \sigma
\rangle$ and $\langle X,\bar \rho \rangle$ are isomorphic. We show that
${\mathbb X}$ is not reversible iff there is a back and forth system $\Pi$ of
partial self-condensations of ${\mathbb X}$ containing one which is not a
partial isomorphism and having certain closure properties. Using that
characterization we detect several classes of non-reversible partial orders
containing, for example, homogeneous-universal posets (in particular, the
random poset), the divisibility lattice, $\langle {\mathbb N}
,\,\mid\,\rangle$, the ideals $[\kappa ]^{<\lambda}$, the meager ideal in the
algebra Borel$(\omega ^\omega)$, and the direct powers of rationals, ${\mathbb
Q} ^\kappa$, and integers, ${\mathbb Z} ^\kappa$. Some of the results are
obtained under additional set-theoretic assumptions.
