Chemical global positioning system

Studies of linear systems and systems without "intermediate interactions show that a positive steady state is unique and stable not only in the "thermodynamic case (closed systems). Horn and Jackson [50] suggested one more class of chemical kinetic equations possessing "quasi-ther-modynamic properties, implying that a positive steady state is unique and stable in a reaction polyhedron and there exist a global (throughout a given polyhedron) Lyapunov function. This class contains equations for closed systems, linear mechanisms, and intersects with a class of equations for "no intermediate interactions reactions, but does not exhaust it. Let us describe the Horn and Jackson approach. 

Michael Baldea is Assistant Professor in the Department of Chemical Engineering at The University of Texas at Austin. Prior to joining The University of Texas, he held industrial research positions with Praxair Technology Center in Tonawanda, NY and GE Global Research in Niskayuna, NY. He has received several research and service awards, including the Model Based Innovation Prize from Process Systems Enterprise and the Best Referee Award from the Journal of Process Control, and has co-authored over 60 papers and presentations. 

These equations have immediate implications for the signs of the /indices. Namely, by the global stability criterion [31, 49] q = 8p/0N > 0, so that any addition of electrons to the system, dN > 0, raises the global chemical potential dp(dN > 0) > 0. Assume that both initial and final states correspond to the global equilibrium, so that dji = djia = djip =. .. > 0. Moreover in a stable molecular system all hardness eigenvalues are positive h > 0, a = 1,..., m. Hence it immediately follows from the EE equations (23) that, for stable systems,... 

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