  Positive loops of Legendrian embeddings are examined from the point of view
of Floer homology of Lagrangian cobordisms. This leads to new obstructions to
the existence of a positive loop containing a given Legendrian, expressed in
terms of the Legendrian contact homology of the Legendrian submanifold. As
applications, old and new examples of orderable contact manifolds are obtained
and discussed. We also show that contact manifolds admitting a filling of a
Liouville domain with non-zero symplectic homology is strongly orderable in the
sense of Liu.
