A new paper with Rory Brittain and Tom Ouldridge:
What would it take to build a thermodynamically reversible Universal Turing machine?
https://t.co/0LXE5ZeTxw
We find a link between halting and energetic cost.
This paper was from a couple of years ago and I think there has been quite a bit of other work on speed limits in the mean time.
A similar result is used in this paper:
https://t.co/f1cxJaXyT9
Recently I've been reading 'Speed Limit for Classical Stochastic Processes' by Shiraishi, Funo and Saito.
https://t.co/fjr2k1X7vK
https://t.co/rHBf5HzaRn
You could then look at modifying the process to increase the efficiency. However, in modifying the process the activity also, in general, changes so the lower bound changes.
A fact about chemical reaction networks that I learnt from https://t.co/efR9ZJvUoD (arXiv: https://t.co/IzhgJa2yP0). For a detailed-balanced network the steady state distribution is a product of Poisson distributions restricted to the reachability class.
This means that if we want the distributions for different species to not independent either the system must be out of equilibrium or the reachability class must be restricted by a conservation law.