Entropy generation during computation - is it really avoidable, even in principle?*

Recent years have seen a resurgence in interest in minimising the thermodynamic costs of computation, driven both by underpinning advances in stochastic thermodynamics and increasing focus on energy efficiency in all aspects of life.  In principle, any operation can be performed in a thermodynamically reversible manner. However, there are a number of challenges associated with performing anything complex enough to be reasonably described as a "computation" when one considers even a highly idealised physical instantiation of the computing device. In this talk I will illustrate these ideas through concrete models of two systems: one that can perform online learning and another capable of universal computation. These models demonstrate the thermodynamic consequences of over-fitting to sampling noise, learning on the fly with finite memory, and the variable halting times of Turing machines. Furthermore, we use these approaches to argue that, although logical reversibility of an operation is not strictly required for thermodynamic reversibility, it is effectively necessary when performing those operations are complex.