Entropy of thought

Back to my speculations about hyper-advanced races sealing themselves off from the rest of the universe.

In his masterpiece "History of the Jove", commonly used as an undergraduate textbook, the capsuleer Uriel Paradisi Anteovnuecci states that there existed a branch of Jove that

lived long lives in perpetual cryogenic slumber, developing a shared virtuality in which the conscious infomorphs of the inhabitants could mingle and conduct research.

It seems to me that in the end they would not even need their physical body, or their brains. Let us for a moment consider a very reductionist view, and ignore the important question of the soul. In that view, the neurons are merely a substrate on which to run an algorithm that changes the state of the infomorph to go from one thought to the next thought. Silicon or other physical substrates could be used to perform the manipulations of informorph data, perhaps faster, or consuming less energy.

There is however a fundamental constraint that can not be circumvented. Every algorithmically computed thought, regardless of the substrate, must create a tiny bit of entropy (I have added a technical note below).

In order to live even a virtual life, also disembodied infomorphs must dump their generated entropy in the big entropy stream that flows from their star into the universe. This fundamental limit does not represent a lot entropy, the bar is pretty low: it will be more than about one picojoule/kelvin for one terabyte of thoughts. But it is not zero.

The question up next is: is it possible to think an infinite amount of thoughts, if you only have access to a finite amount of energy (namely, the energy in the star around which the pure-information beings have secluded themselves)?

Technical note: Information theory tells us that there is entropy being generated by manipulating information. Many types of computational operations can in principle be made adiabatic, but the process of erasing one bit of information always must generate a given (tiny) amount of entropy. Eating up information (erasing it) can power a little heat engine! 

Using qubits does not rescue you from the curse of increasing entropy. There, it is the proces of observing one qubit which breaks the entanglement and turns entanglement entropy into 'thermodynamic' entropy. Again, not all types of operations on qubits generate entropy, but some do, and are inevitable in the course of computation. 

Using trits - or three valued bits - does not help either: while it is true that you need less of them to store a given amount of information, erasing a trit generates more entropy in the same proportion as you gained, leading to the same outcome.