Does heat death of the universe necessarily imply an inability to perform computation? Wikipedia defines the heat death of the universe as follows:

the universe has diminished to a state of no thermodynamic free energy and therefore can no longer sustain processes that consume energy (including computation and life).

I'm actually curious about why computation can't happen without thermodynamic free energy. I'm aware of Landauer's principle, but it seems to me that a closed adiabatic system could still theoretically do internal computational work using some form of computing (perhaps reversible computing).
This system would be closed off from the rest of the universe (e.g. it couldn't have classical inputs or outputs), but it seems like it could still exist and perform computation even in a perfect thermodynamic equilibrium.
Is this form of computation inherently impossible for some reason?
 A: Yes. Energy must be used to perform computation in a way that increases entropy. Otherwise, it would be possible to use computation to reverse entropy- see the Maxwell's Daemon problem. "Reversible computing" was never meant to be completely reversible in the physical sense. Reversible computing only implies that information suffers less entropy than physical particles within the computer.
In order to manipulate a particle in a thermodynmically preferred state (say 0) to a different state (say 1), we need energy available to perform this operation. Furthermore, we must complete the operation in such a way that the "1" state has some stability and requires energy to change, else it would instantly fall back to another state. Thus, the very definition of computation requires irreversible thermodynamic operations.
A: Nature itself does computations and that is how fundamental laws are enforced. As long as some kind of law(s) continue to work in the universe, means universe is able to perform computations. And we know some kind of laws will have to be at work in order to change the state of universe to a state of heat death. How the state of heat death of universe will work, we do not know. That state will be governed by the laws applicable in that state if any. The laws that we know, and question today, may not even be applicable/verifiable in that state of universe.
