Von Neumann-Landauer limit

Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".

Another way of phrasing Landauer's principle is that if an observer loses information about a physical system, the observer loses the ability to extract work from that system.

If no information is erased, computation may in principle be achieved which is thermodynamically reversible, and require no release of heat. This has led to considerable interest in the study of reversible computing.

At 20 °C (room temperature, or 293.15 K), the Landauer limit represents an energy of approximately 0.0172 eV, or 2.75 zJ. Theoretically, room‑temperature computer memory operating at the Landauer limit could be changed at a rate of one billion bits per second with energy being converted to heat in the memory media at the rate of only 2.85 trillionths of a watt (that is, at a rate of only 2.85 pJ/s). Modern computers use millions of times as much energy.

Rolf Landauer first proposed the principle in 1961 while working at IBM. He rigorously justified and stated important limits to an earlier conjecture by John von Neumann. For this reason, it is sometimes referred to as being simply the Landauer bound or Landauer limit.

In 2011 the principle was generalized to show that while information erasure requires an increase in entropy, that increase could theoretically occur at no energy cost (instead, the cost can be taken in another conserved quantity like angular momentum).

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