We present a dynamical interpretation of the Monge–Kantorovich theory in a stationary regime. This new principle, akin to the Fermat principle of geometric optics, captures the geodesic character of many distribution networks such as plant roots, river basins and the physiological transportation network of metabolites in living systems. Our general continuum framework allows us to map a previously proposed phenomenological principle into a stationary Monge optimization principle in the Kantorovich relaxed format.

中文翻译：

---

来自点状源的最佳运输

我们提出了在平稳状态下对蒙格-坎托罗维奇理论的动力学解释。这一新原理类似于几何光学的费马原理，它捕捉了许多分布网络的测地线特征，例如植物根系，河流盆地以及生命系统中代谢物的生理运输网络。我们的通用连续体框架允许我们将先前提出的现象学原理映射为Kantorovich放松格式的平稳Monge优化原理。