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In this paper, we provide a graphic formulation of non-isothermal reactionsystems and show that a non-isothermal detailed balanced network systemconverges (locally) asymptotically to the unique equilibrium within theinvariant manifold determined by the initial condition. To model thermaleffects, the proposed modeling approach extends the classical chemical reactionnetwork by adding two parameters to each direct (reaction) edge, depicting,respectively, the instantaneous internal energy change after the firing of thereaction and the variation of the reaction rate with respect to thetemperature. For systems possessing thermodynamic equilibria, our modelingapproach provides a compact formulation of the dynamics where reaction topologyand thermodynamic information are presented simultaneously. Finally, using thisformulation and the Legendre transformation, we show that non-isothermaldetailed balanced network systems admit some fundamental properties:dissipativeness, the detailed balancing of each equilibrium, the existence anduniqueness of the equilibrium, and the asymptotic stability of eachequilibrium. In general, the analysis and results of this work provide insightsinto the research of non-isothermal chemical reaction systems.

A graphic formulation of non-isothermal chemical reaction systems and the analysis of detailed balanced networks