# Beyond Landauer Erasure

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## Abstract

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**PACS**05.70.-a; 03.65.Ta; 03.67.-a; 89.70.-a

## 1. Introduction

## 2. General Principles for Information Erasure

## 3. Archetypal Erasure Model

**Figure 1.**Energy level diagram for the archetypal erasure model. For clarity, only a few representative energy levels in the continuous energy spectrum of the reservoir are shown. The reservoir and memory remain in thermal equilibrium and exchange energy, while the energy gap between the states of the memory is slowly increased. The size of the circles on each level indicates the relative probabilities of the states.

## 4. Erasure with Multiple Costs

**Figure 2.**Energy and angular momentum diagram for the erasure model with multiple costs. The energy and the z component of the angular momentum of each system has discrete levels in multiples of ε and ℏ, respectively. For convenience, the lowest angular momentum level is labelled with zero angular momentum. To erase the contents of the memory, the reservoir and memory-ancilla systems are allowed to equilibrate by exchanging energy and angular momentum; next, the gap between the states of the memory-ancilla system are increased, and then, the process is repeated.

## 5. Erasure without an Energy Cost

**Figure 3.**Angular momentum diagram for the erasure model without an energy cost. The z component of angular momentum of both systems has discrete levels in multiples of ℏ. All states of both systems are degenerate in energy. The reservoir and memory-ancilla systems are allowed to equilibrate by exchanging angular momentum only; next, the gap between the states of the memory-ancilla system is increased, and then, the process is repeated.

## 6. Discussion

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Barnett, S.M.; Vaccaro, J.A.
Beyond Landauer Erasure. *Entropy* **2013**, *15*, 4956-4968.
https://doi.org/10.3390/e15114956

**AMA Style**

Barnett SM, Vaccaro JA.
Beyond Landauer Erasure. *Entropy*. 2013; 15(11):4956-4968.
https://doi.org/10.3390/e15114956

**Chicago/Turabian Style**

Barnett, Stephen M., and Joan A. Vaccaro.
2013. "Beyond Landauer Erasure" *Entropy* 15, no. 11: 4956-4968.
https://doi.org/10.3390/e15114956