Bob Congdon

In particular, it has been shown that 1 kilogram of matter confined to 1 liter of space can perform at most 10⁵¹ operations per second on at most 10³¹ bits of information ... A fully-populated 128-bit storage pool would contain 2¹²⁸ blocks = 2¹³⁷ bytes = 2¹⁴⁰ bits; therefore the minimum mass required to hold the bits would be (2¹⁴⁰ bits) / (10³¹ bits/kg) = 136 billion kg.

To operate at the 10³¹ bits/kg limit, however, the entire mass of the computer must be in the form of pure energy. By E=mc², the rest energy of 136 billion kg is 1.2x10²⁸ J. The mass of the oceans is about 1.4x10²¹ kg. It takes about 4,000 J to raise the temperature of 1 kg of water by 1 degree Celsius, and thus about 400,000 J to heat 1 kg of water from freezing to boiling. The latent heat of vaporization adds another 2 million J/kg. Thus the energy required to boil the oceans is about 2.4x10⁶ J/kg * 1.4x10²¹ kg = 3.4x10²⁷ J. Thus, fully populating a 128-bit storage pool would, literally, require more energy than boiling the oceans.