  Time periodic modulations of the transverse field in the closed XY spin-1/2
chain generate a very rich dynamical phase diagram, with a hierarchy of
topological phases characterized by differing numbers of Floquet-Majorana
modes. We show that this rich phase diagram survives when the system is coupled
to dissipative end reservoirs. Circumventing the obstacle of preparing and
measuring quasi energy configurations endemic to Floquet-Majorana detection
schemes, we show that stroboscopic heat transport and spin density are robust
observables to detect both the dynamical phase transitions and Majorana modes.
In particular, we find that the derivative of the heat current, with respect to
a control parameter, changes sign at the boundaries separating topological
phases with different numbers of Floquet Majorana modes. We present a simple
scheme to directly count the number of Floquet-Majorana modes in a phase from
the Fourier transform of the local spin density profile. Our results are valid
provided the anisotropies are not strong and can be easily implemented in
quantum engineered systems.
