Limits of computation

There are several physical and practical limits to the amount of computation or data storage that can be performed with a given amount of mass, volume, or energy:

• The Bekenstein Bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area.
• The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvins), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature.

There are several hypotheitcal methods of producing computing devices or data storage devices that approach physical and practical limits:

• A Matrioshka Brain is a set of concentric Dyson spheres that attempts to capture as much usable energy as possible from the host star, to make it available for computation.
• A cold degenerate star could conceivably be used as a giant data storage device, by carefully perturbing it to various excited states, in the same manner as an atom or quantum well used for these purposes. Such a star would have to be artificially constructed, as no natural degenerate stars will cool to this temperature for an extemely long time.
• It may be possible to use black hole as a data storage device, if a practical mechanism for extraction of contained information can be found. Such extraction has been shown to in principle be possible (Stephen Hawking's resolution to the black hole information paradox). This would achieve storage density exactly equal to the Bekenstein Bound.

None of these methods are expected to be practical in the near future.