Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

Abstract

We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial.

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• Optimal control with a strong harmonic trap
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Optimizing power and efficiency of a single spin heat engine
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• Sub-Bath Cooling in Bosonic Systems: Gaussian Constraints and Non-Gaussian Enhancements