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Heat production and error probability relation in Landauer reset at effective temperature

View Article: PubMed Central - PubMed

ABSTRACT

The erasure of a classical bit of information is a dissipative process. The minimum heat produced during this operation has been theorized by Rolf Landauer in 1961 to be equal to kBT ln2 and takes the name of Landauer limit, Landauer reset or Landauer principle. Despite its fundamental importance, the Landauer limit remained untested experimentally for more than fifty years until recently when it has been tested using colloidal particles and magnetic dots. Experimental measurements on different devices, like micro-mechanical systems or nano-electronic devices are still missing. Here we show the results obtained in performing the Landauer reset operation in a micro-mechanical system, operated at an effective temperature. The measured heat exchange is in accordance with the theory reaching values close to the expected limit. The data obtained for the heat production is then correlated to the probability of error in accomplishing the reset operation.

No MeSH data available.


Related in: MedlinePlus

Reset protocol.(a) Protocol used to perform the reset operation. In order to account for all the possible transitions we considered the reset to 1 (first two columns) and reset to 0 (last two columns) starting from both 0 and 1 states. The first row depict the protocol used for removing the barrier. Once the barrier is removed a lateral force is applied (second row). The resulting displacement of the cantilever tip is represented in the third row. Once all the forces are removed and the barrier is restored the cantilever tip encodes the final state. (b) Schematic time evolution of the potential energy and state of the system for the case presented in the first column of panel (a). The operation starts from a double well potential and in the first step of the protocol the barrier is removed. During the next step the potential is tilted and the barrier is restored to its initial value. Finally, the lateral force is removed recovering the initial condition where the barrier between wells is at its maximum and the electrostatic forces are equal to zero.
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f2: Reset protocol.(a) Protocol used to perform the reset operation. In order to account for all the possible transitions we considered the reset to 1 (first two columns) and reset to 0 (last two columns) starting from both 0 and 1 states. The first row depict the protocol used for removing the barrier. Once the barrier is removed a lateral force is applied (second row). The resulting displacement of the cantilever tip is represented in the third row. Once all the forces are removed and the barrier is restored the cantilever tip encodes the final state. (b) Schematic time evolution of the potential energy and state of the system for the case presented in the first column of panel (a). The operation starts from a double well potential and in the first step of the protocol the barrier is removed. During the next step the potential is tilted and the barrier is restored to its initial value. Finally, the lateral force is removed recovering the initial condition where the barrier between wells is at its maximum and the electrostatic forces are equal to zero.

Mentions: Varying the magnets distance d the barrier separating the two stable wells varies from the minimum value B0 for d = 3.65 a.u. to Bmax for d = 2.8 a.u. Applying a voltage on one probe corresponds to apply a force toward the probe itself. Thus a voltage on the left probe corresponds to a negative force and a voltage on the right probe corresponds to a positive force. Details of the force calibration are presented in methods section. In Fig. 2(a) the protocol followed to reset the bit to the state 0 and 1 is presented. The procedure is similar to the ones presented in refs 2 and 9. Initially the barrier separating the two stable states is removed moving the magnet away (red curve in the first panel) making the system monostable. Once the barrier is removed we apply a negative (positive) force to reset the bit status to 0 (1) applying a finite voltage VL (VR) on the left (right) probe. This is represented by the magenta curve in Fig. 2(a). Once the force is applied we restore the barrier to its original value. Finally, we remove the lateral force finishing in the original parameters configuration. At the end of the operation, if there are no errors the cantilever position encodes the desired bit of information. In order to be sure to perform the operation starting from both initial states, we mimic a statistical ensemble where the initial probability is 50% to start in the left well and 50% in the right well. A trace of the cantilever tip position, x, is shown in Fig. 2(a) (black line), where the dashed blue lines represent the two stable positions once the barrier is restored. When the barrier is removed the system goes from the local prepared state to an undefined state with a free expansion, the entropy on the system thus increases in a irreversible manner910. This increment is related to uncontrollable transitions from one well to the other once the barrier height is close to kBT. These large excursions of the cantilever can be seen in the time series of position. Figure 2(b) shows a representation of the time evolution of the potential energy during the set of the bit to the logic state 1. In a first step the barrier is removed allowing the system to oscillate in a monostable potential landscape. Then the potential is slightly tilted and when the barrier is restored the system is confined in the desired state. After these stages the bit is set to the state 1. In order to have a reliable measure of the heat produced during the considered operations, reset protocols are repeated for 800 times in order to have a large enough statistic.


Heat production and error probability relation in Landauer reset at effective temperature
Reset protocol.(a) Protocol used to perform the reset operation. In order to account for all the possible transitions we considered the reset to 1 (first two columns) and reset to 0 (last two columns) starting from both 0 and 1 states. The first row depict the protocol used for removing the barrier. Once the barrier is removed a lateral force is applied (second row). The resulting displacement of the cantilever tip is represented in the third row. Once all the forces are removed and the barrier is restored the cantilever tip encodes the final state. (b) Schematic time evolution of the potential energy and state of the system for the case presented in the first column of panel (a). The operation starts from a double well potential and in the first step of the protocol the barrier is removed. During the next step the potential is tilted and the barrier is restored to its initial value. Finally, the lateral force is removed recovering the initial condition where the barrier between wells is at its maximum and the electrostatic forces are equal to zero.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037424&req=5

f2: Reset protocol.(a) Protocol used to perform the reset operation. In order to account for all the possible transitions we considered the reset to 1 (first two columns) and reset to 0 (last two columns) starting from both 0 and 1 states. The first row depict the protocol used for removing the barrier. Once the barrier is removed a lateral force is applied (second row). The resulting displacement of the cantilever tip is represented in the third row. Once all the forces are removed and the barrier is restored the cantilever tip encodes the final state. (b) Schematic time evolution of the potential energy and state of the system for the case presented in the first column of panel (a). The operation starts from a double well potential and in the first step of the protocol the barrier is removed. During the next step the potential is tilted and the barrier is restored to its initial value. Finally, the lateral force is removed recovering the initial condition where the barrier between wells is at its maximum and the electrostatic forces are equal to zero.
Mentions: Varying the magnets distance d the barrier separating the two stable wells varies from the minimum value B0 for d = 3.65 a.u. to Bmax for d = 2.8 a.u. Applying a voltage on one probe corresponds to apply a force toward the probe itself. Thus a voltage on the left probe corresponds to a negative force and a voltage on the right probe corresponds to a positive force. Details of the force calibration are presented in methods section. In Fig. 2(a) the protocol followed to reset the bit to the state 0 and 1 is presented. The procedure is similar to the ones presented in refs 2 and 9. Initially the barrier separating the two stable states is removed moving the magnet away (red curve in the first panel) making the system monostable. Once the barrier is removed we apply a negative (positive) force to reset the bit status to 0 (1) applying a finite voltage VL (VR) on the left (right) probe. This is represented by the magenta curve in Fig. 2(a). Once the force is applied we restore the barrier to its original value. Finally, we remove the lateral force finishing in the original parameters configuration. At the end of the operation, if there are no errors the cantilever position encodes the desired bit of information. In order to be sure to perform the operation starting from both initial states, we mimic a statistical ensemble where the initial probability is 50% to start in the left well and 50% in the right well. A trace of the cantilever tip position, x, is shown in Fig. 2(a) (black line), where the dashed blue lines represent the two stable positions once the barrier is restored. When the barrier is removed the system goes from the local prepared state to an undefined state with a free expansion, the entropy on the system thus increases in a irreversible manner910. This increment is related to uncontrollable transitions from one well to the other once the barrier height is close to kBT. These large excursions of the cantilever can be seen in the time series of position. Figure 2(b) shows a representation of the time evolution of the potential energy during the set of the bit to the logic state 1. In a first step the barrier is removed allowing the system to oscillate in a monostable potential landscape. Then the potential is slightly tilted and when the barrier is restored the system is confined in the desired state. After these stages the bit is set to the state 1. In order to have a reliable measure of the heat produced during the considered operations, reset protocols are repeated for 800 times in order to have a large enough statistic.

View Article: PubMed Central - PubMed

ABSTRACT

The erasure of a classical bit of information is a dissipative process. The minimum heat produced during this operation has been theorized by Rolf Landauer in 1961 to be equal to kBT ln2 and takes the name of Landauer limit, Landauer reset or Landauer principle. Despite its fundamental importance, the Landauer limit remained untested experimentally for more than fifty years until recently when it has been tested using colloidal particles and magnetic dots. Experimental measurements on different devices, like micro-mechanical systems or nano-electronic devices are still missing. Here we show the results obtained in performing the Landauer reset operation in a micro-mechanical system, operated at an effective temperature. The measured heat exchange is in accordance with the theory reaching values close to the expected limit. The data obtained for the heat production is then correlated to the probability of error in accomplishing the reset operation.

No MeSH data available.


Related in: MedlinePlus