  Polymers consisting of more than one type of monomer, known as copolymers,
are vital to both living and synthetic systems. Copolymerisation has been
studied theoretically in a number of contexts, often by considering a Markov
process in which monomers are added or removed from the growing tip of a long
copolymer. To date, the analysis of the most general models of this class has
necessitated simulation. We present a general method for analysing such
processes without resorting to simulation. Our method can be applied to models
with an arbitrary network of sub-steps prior to addition or removal of a
monomer, including non-equilibrium kinetic proofreading cycles. Moreover, the
approach allows for a dependency of addition and removal reactions on the
neighbouring site in the copolymer, and thermodynamically self-consistent
models in which all steps are assumed to be microscopically reversible. Using
our approach, thermodynamic quantities such as chemical work; kinetic
quantities such as time taken to grow; and statistical quantities such as the
distribution of monomer types in the growing copolymer can be derived either
analytically or numerically directly from the model definition.
