What would it take to build a thermodynamically reversible Universal Turing machine? Computational and thermodynamic constraints in a molecular design.

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.