[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84583-en":3,"doc-seo-84583-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84583,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Fluid Spatiotemporal Stochastic Geometry Information Flow in Non Stationary Fields","Fluid-Spatiotemporal Stochastic Geometry (F-STSG) develops the theoretical limits of information flow in spatial networks when node intensity evolves continuously and non-separably over space and time. It models dynamic topology as a hydrodynamic limit of discrete node constellations, casting latent dynamics identification as an inverse boundary value problem and proving the existence and uniqueness of a governing scalar potential field. The framework yields an Information Flux vector and a Material Derivative predictor for topological divergences, plus scaling laws and a source-channel duality for mobility cost.","Fluid-Spatiotemporal Stochastic Geometry: Information Flow in Non-Stationary Fields  \nWen-Yu Dong, Weiwei Jiang, Senior Member, IEEE, Song Zhao, Qi Bi, Fellow, IEEE, Sheng Chen, Life Fellow, IEEE  \narXiv :2607 .006 16v 1 [ cs .NI] 1 Jul 2026  \nAbstract—The fundamental limits of information flow in spatial networks have been extensively characterized under the assumption of stationary spatial point processes. However, this stationarity hypothesis fails to capture the macroscopic transport of information demand in regimes where the node intensity field exhibits continuous, non-separable spatiotemporal evolution. This paper establishes the theoretical foundations of FluidSpatiotemporal Stochastic Geometry (F-STSG), treating the dynamic topology as a hydrodynamic limit of the discrete node constellation. We formulate the identification of latent network dynamics as an inverse boundary value problem. By invoking the principle of minimum kinetic energy consistent with Optimal Transport theory, we prove the existence and uniqueness of a scalar potential field that strictly governs the compressive evolution of the network load. This field-theoretic formulation establishes a rigorous field-measure coupling between the continuous Lagrangian transport and the discrete Eulerian interference geometry. Based on this, we derive the Information Flux vector, a sufficient statistic for the macroscopic advection of the capacity region, and establish the Material Derivative as the kinematic predictor of topological divergences. Finally, we characterize the fundamental limits of such non-stationary systems through two key theoretical contributions. First, by analyzing the trade-off between spectral efficiency and topological coordination overhead, we derive an asymptotic scaling law for the optimal node density under a quadratic-overhead approximation. We prove that in the interference-limited regime, the energy-optimal topology scales as the square root of the structural cost ratio, defining a thermodynamic inverse-square information barrier independent of linklevel spectral efficiency. Second, we reveal a fundamental sourcechannel duality perspective for mobile networks. By proving that the macroscopic flow divergence mathematically determines the topological entropy production rate, we establish the physical foundation for the information-theoretic cost of mobility. This demonstrates that tracking the dynamic network state requires control signaling capacities that scale fundamentally with the kinematic entropy of the topology.  \nIndex Terms—Stochastic geometry, non-stationary point processes, hydrodynamic limits, inverse problems, scaling laws.  \nI. Introduction  \nCHARACTERIZING the fundamental limits of informa  \ntion flow in stochastic fields is a central problem in network information theory. Classical analyses, from Shannon’s capacity to modern stochastic geometry (SG) [1, 2],  \nW.-Y. Dong, S. Zhao and Q. Bi are with Future Technology Research Center, China Telecom Research Institute, Beijing 102209, China (E-mails: [dongwy@chinatelecom.cn](dongwy@chinatelecom.cn); [zhaosong1@chinatelecom.cn](zhaosong1@chinatelecom.cn); [qibi@chinatelecom.cn](qibi@chinatelecom.cn))  \nW. Jiang is with the School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China (Email: [jww@bupt.edu.cn](jww@bupt.edu.cn))  \nS. Chen is with the School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, U.K., and also with Faculty of Information Science and Technology, Ocean University of China, Qingdao 266100, China (E-mail: [sqc@ecs.soton.ac.uk](sqc@ecs.soton.ac.uk)).  \nare predominantly predicated on the axiom of stationarity. By modeling the spatial configuration of nodes as a realization of a stationary point process, typically a Poisson point process (PPP), these frameworks leverage the ergodic hypothesis to equate time averages with spatial ensemble averages. While t","cbCaiotJY41OUvPT","https://ap.wps.com/l/cbCaiotJY41OUvPT","pdf",2949804,2,1,25,"English","en",105,"# Introduction\n## Stationarity assumption and its limitations\n## Collective mobility as the “Digital Tide”\n## Quasi-static approximations and missing causality\n## Thermodynamic limit and continuum field formulation","[{\"question\":\"What problem does the paper address about information flow modeling?\",\"answer\":\"It targets the fundamental limits of information flow when network node intensity is non-stationary, evolving continuously and non-separably in space and time, which breaks the usual stationary assumptions in classical stochastic geometry.\"},{\"question\":\"How does F-STSG model dynamic network topology?\",\"answer\":\"It treats the dynamic topology as a hydrodynamic limit of a discrete node constellation, introducing a deterministic continuum field that represents collective information-demand transport in the thermodynamic limit.\"},{\"question\":\"What are the key theoretical contributions related to limits and mobility cost?\",\"answer\":\"The paper derives asymptotic scaling laws by analyzing spectral efficiency versus coordination overhead, and establishes a source-channel duality showing that macroscopic flow divergence determines the topological entropy production rate, grounding the information-theoretic cost of mobility in kinematic/topological entropy.\"}]",1784196929,63,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"fluid-spatiotemporal-stochastic-geometry-information-flow-in-non-stationary-fields","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/fluid-spatiotemporal-stochastic-geometry-information-flow-in-non-stationary-fields/84583/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address about information flow modeling?","Question",{"text":75,"@type":76},"It targets the fundamental limits of information flow when network node intensity is non-stationary, evolving continuously and non-separably in space and time, which breaks the usual stationary assumptions in classical stochastic geometry.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does F-STSG model dynamic network topology?",{"text":80,"@type":76},"It treats the dynamic topology as a hydrodynamic limit of a discrete node constellation, introducing a deterministic continuum field that represents collective information-demand transport in the thermodynamic limit.",{"name":82,"@type":73,"acceptedAnswer":83},"What are the key theoretical contributions related to limits and mobility cost?",{"text":84,"@type":76},"The paper derives asymptotic scaling laws by analyzing spectral efficiency versus coordination overhead, and establishes a source-channel duality showing that macroscopic flow divergence determines the topological entropy production rate, grounding the information-theoretic cost of mobility in kinematic/topological entropy.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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