  We examine the heat and charge transport of a driven topological
superconductor. Our particular system of interest consists of a Y-junction of
topological superconducting wires, hosting non-Abelian Majorana zero modes at
their edges. The system is contacted to two leads which act as continuous
detectors of the system state. We calculate, via a scattering matrix approach,
the full counting statistics of the driven heat transport, between two
terminals contacted to the system, for small adiabatic driving and characterise
the energy transport properties as a function of the system parameters (driving
frequency, temperature). We find that the geometric, dynamic contribution to
the pumped heat statistics results in a correction to the Gallavotti-Cohen type
fluctuation theorem for quantum heat transfer. Notably, the correction term to
the fluctuation theorem extends to cycles which correspond to topologically
protected braiding of the Majorana zero modes. This geometric correction to the
fluctuation theorem differs from its analogs in previously studied systems in
that (i) it is non-vanishing for adiabatic cycles of the system's parameters,
without the need for cyclic driving of the leads and (ii) it is insensitive to
small, slow fluctuations of the driving parameters due to the topological
protection of the braiding operation.
