- The paper introduces a Riemannian metric via quantum Fisher information to quantify nonadiabatic entropy production during transitions.
- The study extends the classical Hatano-Sasa relation to open quantum systems, linking excess and housekeeping entropy in NESS transitions.
- The research demonstrates a three-level maser example, providing a framework to engineer minimally dissipative quantum processes.
This paper investigates the transition dynamics between quantum nonequilibrium steady states (NESS) employing an information geometric framework. The research expands on existing thermodynamic theories by exploring the entropy variations and dissipation during these transitions in open quantum systems.
The foundation of this paper lies in the Hatano-Sasa relation, which has predominantly been applied within classical stochastic systems to understand entropy production. The authors extend this framework to the quantum domain, utilizing concepts like excess and housekeeping entropy, which distinguish the entropic cost associated with sustaining steady-state currents from those arising due to the transition itself.
A primary contribution of this paper is a description of the nonadiabatic entropy production using the path action, formulated in terms of a Riemannian metric within the control parameter space. Specifically, this is linked to the Kubo-Mori-Bogoliubov quantum Fisher information (QFI), which serves as a metric to quantify the dissipation paths in such transitions. The paper further illustrates these concepts through a practical example involving a three-level maser system, showing how to engineer minimally dissipative paths by solving the corresponding geodesic equations.
The identification of the quantum Fisher information with respect to time as a metric further enables the derivation of an upper bound on excess entropy flux, applicable even to rapid transitions. This establishes a novel theoretical bridge from slow to arbitrary-speed transitions between NESS using information geometric terms, thereby broadening the applicability of the described framework.
Implications and Future Directions
From a practical standpoint, this work has implications for optimizing quantum processes in technologies such as quantum computing and thermoelectric devices, where controlling dissipation and understanding quantum coherence dynamics are vital. It provides theoretical tools for designing protocols that minimize energy loss, which is critical in developing efficient quantum devices.
Theoretically, the integration of information geometry with quantum thermodynamics offers deeper insights into the entropy dynamics of quantum systems far from equilibrium. By unveiling the role of quantum Fisher information in quantifying dissipation, the paper bridges existing gaps between classical and quantum thermodynamic theories.
Future research directions could explore extending these geometric methods to more complex quantum systems, such as those exhibiting many-body interactions or in states undergoing quantum criticality. Additionally, there is potential for empirical validation of these theoretical predictions, which could further solidify the role of information geometry in the design and control of quantum thermodynamic processes.
In summary, this paper represents a methodological advancement in our understanding of quantum thermodynamics, offering a cohesive framework for analyzing transitions between quantum NESS from a geometric perspective. It sets a foundation for future theoretical explorations and practical applications in the optimization of quantum processes and technologies.