  Living systems produce "persistent" copies of information-carrying polymers,
in which template and copy sequences remain correlated after physically
decoupling. We identify a general measure of the thermodynamic efficiency with
which these non-equilibrium states are created, and analyze the accuracy and
efficiency of a family of dynamical models that produce persistent copies. For
the weakest chemical driving, when polymer growth occurs in equilibrium, both
the copy accuracy and, more surprisingly, the efficiency vanish. At higher
driving strengths, accuracy and efficiency both increase, with efficiency
showing one or more peaks at moderate driving. Correlations generated within
the copy sequence, as well as between template and copy, store additional free
energy in the copied polymer and limit the single-site accuracy for a given
chemical work input. Our results provide insight in the design of natural
self-replicating systems and can aid the design of synthetic replicators.
