  We outline the construction of a molecular system that could, in principle,
implement a thermodynamically reversible Universal Turing Machine (UTM). By
proposing a concrete-albeit idealised-design and operational protocol, we
reveal fundamental challenges that arise when attempting to implement arbitrary
computations reversibly. Firstly, the requirements of thermodynamic
reversibility inevitably lead to an intricate design. Secondly,
thermodynamically reversible UTMs, unlike simpler devices, must also be
logically reversible. Finally, implementing multiple distinct computations in
parallel is necessary to take the cost of external control per computation to
zero, but this approach is complicated the distinct halting times of different
computations.
