[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84275-en":3,"doc-seo-84275-105":29,"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84275,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Thermodynamic Structure and Composition in Nonlinear Convection–Diffusion","Nonlinear convection–diffusion systems govern transport phenomena spanning mass transfer, heat transfer, porous-media transport, and coupled continuum processes with sources, exchange, and interface effects. The work addresses whether thermodynamic balance is preserved by natural model operations such as subdomain restriction, interface coupling, equilibrium linearization, and computational discretization. A continuum-first framework is developed using a free-energy balance with nonnegative bulk dissipation and explicit boundary/source contributions, proving invariance under structure-preserving transformations, reconstruction, and power-conserving interconnections.","arXiv :2607 .07829v1 [math .NA] 8 Jul 2026  \nThermodynamic Structure and Composition in Nonlinear  \nConvection–Diffusion  \nJ. J. Segura  \nPublication note. This manuscript is the author-prepared arXiv version of the article published in Open Transport. The Version of Record is available at DOI: 10.1515/ot-2026-0013 .  \nAbstract  \nNonlinear convection–diffusion systems play a central role in transport phenomena, including mass transfer, heat transfer, porous-media transport, and coupled continuum processes with source, exchange, and interface effects. In such systems, the key question is often not only which governing partial differential equation is used, but whether the model preserves a consistent thermodynamic balance under the operations that arise naturally in transport analysis: restriction to subdomains, coupling across interfaces, linearization near equilibrium, and discretization for computation.  \nThis paper develops a continuum-first framework for open nonlinear convection–diffusion systems in which thermodynamic consistency is formulated as a free-energy balance with nonnegative bulk dissipation and explicit boundary and source contributions. Within this setting, nonlinear transport systems are defined as structured objects built from admissible state fields, storage functionals, constitutive flux decompositions, sources, and boundary ports. We prove that the thermodynamic balance is preserved under exact structure-preserving transformations, restriction to subdomains, local-to-global reconstruction over compatible domain decompositions, and power-conserving interconnection of open subsystems. We then derive classical linear convection–diffusion models as tangent thermodynamic descendants at equilibrium and show that the same invariant survives weak formulation, semidiscretization, and fully discrete time stepping when the numerical design respects thermodynamic structure. Nonlinear drift–diffusion and porous-medium convection–diffusion are used as explicit examples. The resulting contribution is a compositional transport framework in which the second law remains visible across continuum modeling, subsystem coupling, linear approximation, and computation.  \nKeywords: nonlinear convection–diffusion; thermodynamic consistency; free-energy balance; transport phenomena; subsystem coupling; local-to-global reconstruction; structure-preserving discretization  \nMSC 2020: 35K65, 35K55, 76R50, 80A20, 65M12  \n1 Introduction  \nNonlinear convection–diffusion systems lie at the core of transport phenomena. They govern the coupled movement of mass, heat, and generalized scalar quantities in fluids, porous media, reactive continua, and multiscale engineering systems. In such problems, convection, diffusion, source terms, and boundary exchange do not merely coexist; they interact in ways that strongly affect admissibility, stability, and physical interpretation. For this reason, a satisfactory transport model should do more than reproduce a governing differential equation. It should also preserve the relevant thermodynamic  \nbalance, especially when the system is restricted to a subdomain, coupled to another subsystem across an interface, linearized near an equilibrium state, or discretized for computation.  \nSeveral existing traditions address parts of this structural problem. Classical nonequilibrium thermodynamics emphasizes constitutive consistency and entropy production [1, 2 , 3]; gradient-flow and energy–dissipation approaches clarify nonlinear relaxation and free-energy decay [6, 7 , 9 , 10]; and open-system or boundary-energy formulations make exchange with the environment mathematically explicit [11 , 4 , 5] . The present paper takes a complementary route tailored to nonlinear continuum transport. We treat open convection–diffusion systems as primitive thermodynamic objects and study which natural transport operations preserve thermodynamic consistency. This leads to a categorical formulation, but the motivation remains ","cbCaiqCrylZeCPqg","https://ap.wps.com/l/cbCaiqCrylZeCPqg","pdf",438025,1,22,"English","en",105,"# Introduction\n## Main contributions","[{\"question\":\"What key issue does the paper address for nonlinear convection–diffusion models?\",\"answer\":\"The paper focuses on whether a model preserves a consistent thermodynamic balance under operations naturally used in transport analysis, including restriction, interface coupling, linearization near equilibrium, and discretization.\"},{\"question\":\"How does the proposed framework define thermodynamic consistency?\",\"answer\":\"Thermodynamic consistency is formulated as a free-energy balance with nonnegative bulk dissipation, together with explicit boundary and source contributions.\"},{\"question\":\"Which transformations are proven to preserve the thermodynamic balance?\",\"answer\":\"The paper proves preservation under exact structure-preserving transformations, subdomain restriction, local-to-global reconstruction for compatible decompositions, and power-conserving interconnection of open 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key issue does the paper address for nonlinear convection–diffusion models?","Question",{"text":75,"@type":76},"The paper focuses on whether a model preserves a consistent thermodynamic balance under operations naturally used in transport analysis, including restriction, interface coupling, linearization near equilibrium, and discretization.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed framework define thermodynamic consistency?",{"text":80,"@type":76},"Thermodynamic consistency is formulated as a free-energy balance with nonnegative bulk dissipation, together with explicit boundary and source contributions.",{"name":82,"@type":73,"acceptedAnswer":83},"Which transformations are proven to preserve the thermodynamic balance?",{"text":84,"@type":76},"The paper proves preservation under exact structure-preserving transformations, subdomain restriction, local-to-global reconstruction for compatible decompositions, and power-conserving interconnection of open 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