Recent advances in nonequilibrium statistical mechanics have led to a deeper understanding of the thermodynamic cost of computation than that put forth by Landauer and then studied extensively in the computational complexity community. In particular, Landauer's work led to a focus on the number of bit erasures in a computation, due to its relation to the change in entropy between input and output. However new advances in physicswhich have been experimentally con rmedmean we can now calculate additional thermodynamic costs beyond merely the change in entropy between input and output. As a consequence, we now understand that while logically reversible computing can have some thermodynamic bene ts, it is far from the end of the story. The purpose of this paper is to highlight new open questions in computational complexity raised by consideration of these new thermodynamic costs. Beyond leading to a revised viewpoint on the bene ts of logical reversibility, these questions touch on randomized algorithms, average-case complexity, the thermodynamic cost of error correcting codes, and noisy/inexact/approximate computation.