TY - JOUR
AB - 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.
AU - Brooks, Morris
AU - Maas, Jan
ID - 17282
IS - 6
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
TI - Characterisation of gradient flows for a given functional
VL - 63
ER -