  Living cells use readout molecules to record the state of receptor proteins,
similar to measurements or copies in typical computational devices. But is this
analogy rigorous? Can cells be optimally efficient, and if not, why? We show
that, as in computation, a canonical biochemical readout network generates
correlations; extracting no work from these correlations sets a lower bound on
dissipation. For general input, the biochemical network cannot reach this
bound, even with arbitrarily slow reactions or weak thermodynamic driving. It
faces an accuracy-dissipation trade-off that is qualitatively distinct from and
worse than implied by the bound, and more complex steady-state copy processes
cannot perform better. Nonetheless, the cost remains close to the thermodynamic
bound unless accuracy is extremely high. Additionally, we show that
biomolecular reactions could be used in thermodynamically optimal devices under
exogenous manipulation of chemical fuels, suggesting an experimental system for
testing computational thermodynamics.
