# Hacking Landauer

In 1961, Rolf Landauer in his article “Irreversibility and heat generation in the computing process” formulated the principle that in any computer system, regardless of its physical implementation, if 1 bit of information is lost, heat is released in an amount of at least W = k B T ln2 , where k B is the Boltzmann constant, and T is the temperature of the computing system in kelvins.

That is, if the calculation is performed at room temperature (300K), then with the loss of 1 bit of data, the computer system cannot but dissipate approximately 2.7 × 10 -21 J into the surrounding space .

It is believed that the only way to overcome this limitation is to use so-called reversible calculations . In this article I will prove that the Landauer principle is not a dogma, and it is possible to overcome the barrier it establishes, even without the use of reversible calculations.

## Where did the restriction come from

The key to understanding what the Landauer principle implies is in the phrase " a bistable potential well " (the simplest binary device consists of a particle in a two-stable potential well):

In order to switch the system from state “0” to state “1” (or vice versa), we must:

1. Give the particle enough energy to overcome the barrier.
2. To take energy from a particle so that the particle locks into a new position.

If we use reversible calculations, then the extracted energy is transferred to the next element in the chain of calculations, but if our calculations are irreversible, we are obliged to dissipate the excess energy into the surrounding space in the form of non-recyclable heat.

## We overcome the limitation

Let us proceed from the fact that all the above arguments are correct (the community had enough time to check all theoretical calculations since 1961), and, as a result, for the case of a two-stable potential well, the formula W = k B T ln2 is correct .

To overcome the limitation, instead of a binary data coding system, quaternary is applicable. The scheme of the device will change accordingly:

We still need to give the particle energy to switch the state to overcome the barrier and still have to (in the case of irreversible calculations) dissipate the excess energy in the form of heat. Only now the energy W is spent not on one bit of data, but on two. Thus, when recalculating to one bit, the formula now looks like this:

W = k B T ln2 / 2

Landauer's barrier was reduced exactly twice. If the system does not make 4 potential pits, but 8, then the required energy dissipation becomes W = k B T ln2 / 3. In the limiting case, when the number of potential pits rushes to infinity (I can’t imagine how , but in theory this has the right to exist) Landauer's barrier rushes to zero.

## Conclusion

Until now, the Landauer principle was considered as an insurmountable fundamental constraint imposed on the increase in computing power, but it turned out that it was a consequence of the choice of a variant of the computing system architecture. Namely, separate coding of data bits by system elements.

UPD (necessary clarification, thanks Pshir ): please pay attention to this comment chain: thisthisand this one .