Fluid-Spatiotemporal Stochastic Geometry: Information Flow in Non-Stationary Fields
2026-07-01 • Networking and Internet Architecture
Networking and Internet Architecture
AI summaryⓘ
The authors study how information moves in networks where the positions and number of nodes change over space and time, not just stay fixed. They create a new mathematical model, Fluid-Spatiotemporal Stochastic Geometry, which treats these changing networks like flowing fluids. By linking physical principles of energy use with network behavior, the authors find a unique way to describe how information spreads and network connectivity evolves. They also explain how aspects like control signals and network coordination relate to changes in the network's shape and complexity over time.
spatial networksstochastic geometryhydrodynamic limitinverse boundary value problemoptimal transportLagrangian transportEulerian geometryinformation fluxtopological divergencekinematic entropy
Authors
Wen-Yu Dong, Weiwei Jiang, Song Zhao, Qi Bi, Sheng Chen
Abstract
The fundamental limits of information flow in spatial networks are usually characterized under stationary spatial point processes, but this assumption cannot capture non-stationary regimes where the node intensity field evolves continuously in space and time. This paper develops Fluid-Spatiotemporal Stochastic Geometry (F-STSG), treating dynamic network topology as a hydrodynamic limit of the discrete node constellation. We formulate the identification of latent network dynamics as an inverse boundary value problem and, using the minimum kinetic energy principle from optimal transport, establish the existence and uniqueness of a scalar potential field governing the compressive evolution of network load. The resulting field-theoretic formulation couples continuous Lagrangian transport with discrete Eulerian interference geometry. Based on this model, we derive the information flux vector as a sufficient statistic for macroscopic advection and the material derivative as a kinematic predictor of topological divergence. We further characterize non-stationary network limits through energy-density scaling and source-channel interpretation, showing how coordination overhead, topology deformation, and control signaling requirements are linked to the kinematic entropy of the evolving network topology.