  We introduce a numerical method to sample the distributions of charge, heat,
and entropy production in open quantum systems coupled strongly to macroscopic
reservoirs, with both temporal and energy resolution and beyond the
linear-response regime. Our method exploits the mesoscopic-leads formulation,
where macroscopic reservoirs are modeled by a finite collection of modes that
are continuously damped toward thermal equilibrium by an appropriate
Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on
non-interacting fermionic systems, we access the time-resolved full counting
statistics through a trajectory unraveling of the master equation. We show that
the integral fluctuation theorems for the total entropy production, as well as
the martingale and uncertainty entropy production, hold. Furthermore, we
investigate the fluctuations of the dissipated heat in finite-time information
erasure. Conceptually, our approach extends the continuous-time trajectory
description of quantum stochastic thermodynamics beyond the regime of weak
system-environment coupling.
