Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Primary Amine–2-Aminopyrimidine Chiral Organocatalysts for the Enantioselective Conjugate Addition of Branched Aldehydes to Maleimides

Chiral primary amines containing the (R,R)- and (S,S)-trans-cyclohexane-1,2-diamine scaffold and a pyrimidin-2-yl unit are synthesized and used as general organocatalysts for the Michael reaction of α-branched aldehydes to maleimides. The reaction takes place with 10 mol% organocatalyst loading and hexanedioic acid as cocatalyst in aqueous N,N-dimethylformamide at 10 °C affording the corresponding succinimides in good yields and enantioselectivities. DFT calculations support the stereochemical results and the role played by the solvents.

Bifunctional primary amine 2-aminobenzimidazole organocatalyst anchored to trans-cyclohexane-1,2-diamine in enantioselective conjugate additions of aldehydes

Bifunctional chiral primary amine 8 containing an (S,S)-trans-cyclohexane-1,2-diamine scaffold and a 2-benzimidazole unit is used as a general organocatalyst for the Michael addition of α,α-branched aldehydes to nitroalkenes and maleimides. The reactions take place, with 20 mol % of catalyst in dichloromethane at rt for nitroalkenes and with 15 mol % catalyst loading in toluene at 10 °C for maleimides, in good yields and enantioselectivities. DFT calculations demonstrate the bifunctional character of this organocatalyst activating the aldehyde by enamine formation and the Michael acceptor by double hydrogen bonding.