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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?

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    $\begingroup$ Computing means that you go from a state of low information to one of higher information, i.e. you have to select a specific microscopic state. A closed system can't do that. All microscopic states (that satisfy the conservation laws) are physically equivalent. Apart from that... the programmer won't be around, either, so there is little point in running a program. Adding the magic words "quantum mechanics" doesn't change anything about any of this. $\endgroup$
    – CuriousOne
    Feb 27 '16 at 21:28
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    $\begingroup$ I've removed the bit about quantum computing, as I think you are correct that this makes the question less clear. I also see that I may not be using the correct definition of computing. I'm asking if a system can exist that is isolated in terms of energy, matter, and information that was designed to perform some computation repeatedly (albeit uselessly from the perspective of an outside observer). $\endgroup$
    – jncraton
    Feb 28 '16 at 0:09
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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.

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    $\begingroup$ "Energy must be consumed to ...". Total energy is constant over time. I don't understand your answer. $\endgroup$ Feb 27 '16 at 23:52
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    $\begingroup$ @GyroGearloose Read as "Usable energy must be consumed". It's true that energy is never created or destroyed, but it does change form and may not be in a form that is usable in any way. $\endgroup$ Feb 29 '16 at 20:32
  • $\begingroup$ If everything was in thermal equilibrium, then there would certainly be no usable thermal energy, but does that necessarily mean that there's no usable gravitational / chemical / electromagnetic energy? What if there was an advanced kind of computer made of superconductors / photonics / time crystals that had no dependence on mechanical energy? $\endgroup$
    – Derwent
    Jul 11 '20 at 1:57
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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.

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    $\begingroup$ "Nature itself does computations and that is how fundamental laws are enforced." [citation needed] That we describe the universe by mathematical models implies in no way that the universe "actually performs" (whatever that even means) computations. $\endgroup$
    – ACuriousMind
    Feb 28 '16 at 23:38
  • $\begingroup$ @ACuriousMind: How does nature/universe know what should be the next state, unless it knows the current state, and the rules. When you put two charges close, universe decides what needs to happen to these charges (attraction/repulsion, how much..). As long as the state of the universe keeps changing, there are computations happening on what the next state should be. When there is not change in state, there is also a computation that there should be no change in state. What I mean by computation is workings of the fundamental laws applicable to current state of universe at any time. $\endgroup$
    – kpv
    Mar 1 '16 at 18:30

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