  We perform the first study on asymmetric longitudinal decorrelations of
elliptic, triangular and quadrangular flows in proton-nucleus collisions at the
LHC and RHIC energies. To measure the longitudinal flow decorrelations for
asymmetric collision systems, we propose a new set of rapidity-asymmetric flow
decorrelation functions. Our event-by-event hydrodynamic calculations show that
the flow decorrelations in proton-going direction are larger than those in
nucleus-going direction. We also find that proton-nucleus collisions at RHIC
have larger longitudinal flow decorrelation effects than those at the LHC. Our
study opens a new window to probe the longitudinal properties and the origin of
flows in relativistic nuclear collisions.
