If we need to use a Turing machine which is roughly equivalent to physics, then a natural next step is to drop the assumption that the machine in question is Turing complete. Just pick some class of machines which can efficiently simulate our physics, and which can be efficiently implemented in our physics. And then, one might hope, the sort of algorithmic thermodynamic theory the paper presents can carry over to that class of machines.
Probably there are some additional requirements for the machines, like some kind of composability, but I don’t know exactly what they are.
This would also likely result in a direct mapping between limits on the machines (like e.g. limited time or memory) and corresponding limits on the physical systems to which the theory applies for those machines.
The resulting theory would probably read more like classical thermo, where we’re doing thought experiments involving fairly arbitrary machines subject to just a few constraints, and surprisingly general theorems pop out.
What I have in mind re:boundedness...
If we need to use a Turing machine which is roughly equivalent to physics, then a natural next step is to drop the assumption that the machine in question is Turing complete. Just pick some class of machines which can efficiently simulate our physics, and which can be efficiently implemented in our physics. And then, one might hope, the sort of algorithmic thermodynamic theory the paper presents can carry over to that class of machines.
Probably there are some additional requirements for the machines, like some kind of composability, but I don’t know exactly what they are.
This would also likely result in a direct mapping between limits on the machines (like e.g. limited time or memory) and corresponding limits on the physical systems to which the theory applies for those machines.
The resulting theory would probably read more like classical thermo, where we’re doing thought experiments involving fairly arbitrary machines subject to just a few constraints, and surprisingly general theorems pop out.