Characterizing the Asymmetry in Hardness between Synthesis and Destruction of Heteropolymers

Abstract

We present a simple model describing the assembly and disassembly of heteropolymers consisting of two types of monomers A and B. We prove that no matter how we manipulate the concentrations of A and B, it takes longer than the exponential function of d to synthesize a fixed amount of the desired heteropolymer, where d is the number of A−B connections. We also prove the decomposition time is linear for chain length n. When d is proportional to n, synthesis and destruction have an exponential asymmetry. Our findings may facilitate research on the more general asymmetry of operational hardness.