@article{17282,
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.},
author = {Brooks, Morris and Maas, Jan},
issn = {1432-0835},
journal = {Calculus of Variations and Partial Differential Equations},
number = {6},
publisher = {Springer Nature},
title = {{Characterisation of gradient flows for a given functional}},
doi = {10.1007/s00526-024-02755-z},
volume = {63},
year = {2024},
}