Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

This is the final version. Available on open access from IOP Publishing via the DOI in this recordData availability statement; All data that support the findings of this study are included within the article (and any supplementary files).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.Humboldt FoundationCzech Science Foundation'la Caixa' FoundationGovernment of SpainSevero OchoaFundacio CellexFundacio Mir-PuigGeneralitat de CatalunyaFundational Questions Institute FundEngineering and Physical Sciences Research Council (EPSRC)China Scholarship CouncilSwiss National Science Foundatio