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Updated: Jun 22, 2025

A Gradient-generating Microfluidic Device for Cell Biology
Published on: August 30, 2007
Characterisation of gradient flows for a given functional
1Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
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 on M such that ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we provide a gradient-flow characterisation for dissipative quantum systems. Namely, we show that finite-dimensional ergodic Lindblad equations admit a gradient flow structure for the von Neumann relative entropy if and only if the condition of bkm-detailed balance holds.
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