In dynamic combinatorial libraries, molecules react with each other reversibly to form intricate networks under thermodynamic control. In biological systems, chemical reaction networks operate under kinetic control by the transduction of chemical energy. We thus introduced the notion of energy transduction, via chemical reaction cycles, to a dynamic combinatorial library. In the library, monomers can be oligomerized, oligomers can be deoligomerized, and oligomers can recombine. Interestingly, we found that the dynamics of the library's components were dominated by transacylation, which is an equilibrium reaction. In contrast, the library's dynamics were dictated by fuel-driven activation, which is a nonequilibrium reaction. Finally, we found that self-assembly can play a large role in affecting the reaction's kinetics via feedback mechanisms. The interplay of the simultaneously operating reactions and feedback mechanisms can result in hysteresis effects in which the outcome of the competition for fuel depends on events that occurred in the past. In future work, we envision diversifying the library by modifying building blocks with catalytically active motifs and information-containing monomers.