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.

arXiv comment5 pages, 3 figures

References in corpus (10)

• Ising formulations of many NP problems
• Thermodynamic uncertainty relation for biomolecular processes
• Information heat engine: converting information to energy by feedback control
• The Bethe lattice spin glass revisited
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Undecidability of the Spectral Gap (short version)
• Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
• Speed Limit for Classical Stochastic Processes
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• Constructor Theory of Life