Characterisation of gradient flows for a given functional
Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153.
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Abstract
Let X be a vector field and Y be a co-vector field on a smooth manifold M. Does there exist a smooth Riemannian metric gαβ on M such that Yβ=gαβXα ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we show that a finite-dimensional ergodic Lindblad equation admits a gradient flow structure for the von Neumann relative entropy if and only if the condition of BKM-detailed balance holds.
Publishing Year
Date Published
2024-07-01
Journal Title
Calculus of Variations and Partial Differential Equations
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria).J. M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB F65. We thank the anonymous referee for valuable comments on the paper.
Volume
63
Issue
6
Article Number
153
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IST-REx-ID
Cite this
Brooks M, Maas J. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 2024;63(6). doi:10.1007/s00526-024-02755-z
Brooks, M., & Maas, J. (2024). Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-024-02755-z
Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2024. https://doi.org/10.1007/s00526-024-02755-z.
M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,” Calculus of Variations and Partial Differential Equations, vol. 63, no. 6. Springer Nature, 2024.
Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153.
Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” Calculus of Variations and Partial Differential Equations, vol. 63, no. 6, 153, Springer Nature, 2024, doi:10.1007/s00526-024-02755-z.
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