Informational steady states and conditional entropy production in continuously monitored systems: The case of Gaussian systems

The act of measuring a system has profound consequences dynamical and thermodynamic nature. In particular, the degree irreversibility ensuing from non-equilibrium process is strongly affected by measurements aimed at acquiring information on state interest: conditional unconditional entropy production, which quantify open system's dynamics, are related to each other clearly interpreted informational quantities. Building recently proposed collisional-model framework [G. T. Landi {\it et al.}, arXiv:2103.06247], we investigate case continuous-variable carriers prepared in Gaussian states undergoing processes. We build up toolbox that fully characterizes thermodynamics continuously measured systems processes, illustrating how instruments hereby introduced provide key insight into recent experiments mesoscopic quantum [Phys. Rev. Lett, {\bf 125}, 080601 (2020)].