Thermodynamic properties of quantum trajectories

Investigate the thermodynamic properties of quantum trajectories in continuously monitored quantum systems, establishing consistent trajectory-level definitions and measurements of entropy, work, and heat.

Background

Quantum trajectories—stochastic evolutions conditioned on continuous measurements—are central to modern quantum control, thermodynamics, and metrology. While their dynamics are well understood, the thermodynamic interpretation at the individual-trajectory level faces conceptual challenges due to coherence, measurement back-action, and Bayesian conditioning.

Clarifying the trajectory-level meaning of thermodynamic quantities would bridge experimentally accessible stochastic records with thermodynamic resource accounting, and inform practical cooling, control, and feedback strategies.

References

Even though quantum trajectories are, by now, fairly well understood, there are still several open questions concerning their thermodynamic properties.

— Roadmap on Quantum Thermodynamics  (2504.20145 - Campbell et al., 28 Apr 2025) in Section 11, Thermodynamics of quantum trajectories — State-of-the-art

Much is left to be understood (and to be calculated). We mention two important open questions. First, it would be useful to generalize notions of frenesy to the quantum world.

— Entropy and Frenesy: the arrow and the bustle of time  (2608.17586 - Maes, 18 Aug 2026) in Section “Main thesis and open questions” (Section \ref{math})