Informational Steady States and Conditional Entropy Production in Continuously Monitored Systems

We put forth a unifying formalism for the description of thermodynamics continuously monitored systems, where measurements are only performed on environment connected to system. show, in particular, that conditional and unconditional entropy production, which quantify degree irreversibility open system’s dynamics, related each other by Holevo quantity. This, turn, can be further split into an information gain rate loss rate, provide conditions existence informational steady states, i.e., stationary states dynamics maintained owing unbroken acquisition information. illustrate applicability our framework through several examples.Received 25 March 2021Accepted 10 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010303Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasOpen quantum systemsQuantum thermodynamicsStatistical PhysicsQuantum Information