  Pipelining is a design technique for logical circuits that allows for higher
throughput than circuits in which multiple computations are fed through the
system one after the other. It allows for much faster computation than
architectures in which inputs must pass through every layer of the circuit
before the next computation can begin (phased chaining). We explore the
hypothesis that these advantages may be offset by a higher error rate, logical
irreversibility and greater thermodynamic costs by simulating pipelined
molecular mechanical circuits using an explicit physical model. We observe the
emergent logical irreversibility, and see that the simultaneous action of
multiple components indeed leads to a higher error rate than in phase-chained
circuits. The thermodynamic costs of operating the gates are much larger than
in equivalent phase-chained circuits, and these costs do not appear to tend to
zero in the limit of slow gate operation. Redesigning the gates to eliminate
errors and artificially enforcing logical reversibility reduces the
thermodynamic costs and recovers thermodynamically reversible behaviour in the
limit of slow gate operation. The breakdown of logical reversibility and
accuracy are both associated with a breakdown of the digital behaviour of the
device, likely contributing to thermodynamic costs that are large relative to
the scale of the information being processed.
