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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.

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Produced heat and probability of success for the reset operation.(a) Average heat produced during the reset operation as function of the lateral alignment Δx. For Δx < 0 the counter magnet is moved to the right and the 0 state (x < 0) is favorable. Accordingly, for Δx > 0 the 1 state is more favorable. Introducing an asymmetry on the potential Q decreases, which is accounted to the probability of success, Ps, that tends to decrease (Ps is encoded in the color map). (b) Success rate of the reset operation as function of lateral alignment. Solid violet circles represent the overall success rate while black and red symbols account for the success rate resetting to 0 and 1 state respectively. The maximum overall success rate is present when the system is almost symmetric, Δx ≈ 0. (c) Relation between success rate and heat dissipated. Red circles correspond to the resetting to 1 case while black ones correspond to the resetting to 0. (d) Dependence of Q with the protocol time duration, τp. As τp is increased the effects of frictional phenomena becomes negligible and the produced heat should approach the thermodynamic limit. However, for large τp the reset operation fails giving a wrong logic output. In these cases, where the error probability is high, the produced heat is clearly below the Landauer limit. Inset shows the obtained relation between error probability (1 − Ps) and produced heat. The data are compatible with the minimum energy required for a given error probability as predicted by Eq. 1, represented by dashed line.
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f3: Produced heat and probability of success for the reset operation.(a) Average heat produced during the reset operation as function of the lateral alignment Δx. For Δx < 0 the counter magnet is moved to the right and the 0 state (x < 0) is favorable. Accordingly, for Δx > 0 the 1 state is more favorable. Introducing an asymmetry on the potential Q decreases, which is accounted to the probability of success, Ps, that tends to decrease (Ps is encoded in the color map). (b) Success rate of the reset operation as function of lateral alignment. Solid violet circles represent the overall success rate while black and red symbols account for the success rate resetting to 0 and 1 state respectively. The maximum overall success rate is present when the system is almost symmetric, Δx ≈ 0. (c) Relation between success rate and heat dissipated. Red circles correspond to the resetting to 1 case while black ones correspond to the resetting to 0. (d) Dependence of Q with the protocol time duration, τp. As τp is increased the effects of frictional phenomena becomes negligible and the produced heat should approach the thermodynamic limit. However, for large τp the reset operation fails giving a wrong logic output. In these cases, where the error probability is high, the produced heat is clearly below the Landauer limit. Inset shows the obtained relation between error probability (1 − Ps) and produced heat. The data are compatible with the minimum energy required for a given error probability as predicted by Eq. 1, represented by dashed line.

Mentions: In Fig. 3(a) we present the average heat produced for the reset operation as function of the lateral alignment of the counter magnet Δx. When the system is aligned closely to perfection (i.e., Δx ≈ 0) we estimate a heat production slightly above kBT and below two times QL. Asymmetrizing the potential, by means of setting Δx ≠ 0, the heat produced tends to decrease reaching values this time below QL. However, in this conditions the error rate in performing the reset operation have a major role, in fact in this configuration the probability of success, Ps, decrease rapidly. This is represented by the color map of dots in Fig. 3(a), where green represents higher success rate while blue represents a higher probability of error. In Fig. 3(b) the success rate of the reset operation is reported as function of the lateral alignment. Solid violet circles represent the overall success rate while red and black symbols represent the error rate for resetting to 1 or to 0 respectively. Circles are used to report the error probability for the same initial and final state while crosses are used for 0 to 1 and 1 to 0 transitions. For instance let us consider the case where Δx < 0: the counter magnet is moved towards the right and as a consequence the 0 state is more favorable respect the 1 state. From Fig. 3(b) we can see that for Δx < 0 the probability of resetting toward 0 is almost 100% while the probability of resetting toward 1 decreases rapidly reaching values below 50%. The same behavior is present in the case Δx > 0, where the counter magnet is moved to the left, where the state 1 is more favorable.


Heat production and error probability relation in Landauer reset at effective temperature
Produced heat and probability of success for the reset operation.(a) Average heat produced during the reset operation as function of the lateral alignment Δx. For Δx < 0 the counter magnet is moved to the right and the 0 state (x < 0) is favorable. Accordingly, for Δx > 0 the 1 state is more favorable. Introducing an asymmetry on the potential Q decreases, which is accounted to the probability of success, Ps, that tends to decrease (Ps is encoded in the color map). (b) Success rate of the reset operation as function of lateral alignment. Solid violet circles represent the overall success rate while black and red symbols account for the success rate resetting to 0 and 1 state respectively. The maximum overall success rate is present when the system is almost symmetric, Δx ≈ 0. (c) Relation between success rate and heat dissipated. Red circles correspond to the resetting to 1 case while black ones correspond to the resetting to 0. (d) Dependence of Q with the protocol time duration, τp. As τp is increased the effects of frictional phenomena becomes negligible and the produced heat should approach the thermodynamic limit. However, for large τp the reset operation fails giving a wrong logic output. In these cases, where the error probability is high, the produced heat is clearly below the Landauer limit. Inset shows the obtained relation between error probability (1 − Ps) and produced heat. The data are compatible with the minimum energy required for a given error probability as predicted by Eq. 1, represented by dashed line.
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Related In: Results  -  Collection

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f3: Produced heat and probability of success for the reset operation.(a) Average heat produced during the reset operation as function of the lateral alignment Δx. For Δx < 0 the counter magnet is moved to the right and the 0 state (x < 0) is favorable. Accordingly, for Δx > 0 the 1 state is more favorable. Introducing an asymmetry on the potential Q decreases, which is accounted to the probability of success, Ps, that tends to decrease (Ps is encoded in the color map). (b) Success rate of the reset operation as function of lateral alignment. Solid violet circles represent the overall success rate while black and red symbols account for the success rate resetting to 0 and 1 state respectively. The maximum overall success rate is present when the system is almost symmetric, Δx ≈ 0. (c) Relation between success rate and heat dissipated. Red circles correspond to the resetting to 1 case while black ones correspond to the resetting to 0. (d) Dependence of Q with the protocol time duration, τp. As τp is increased the effects of frictional phenomena becomes negligible and the produced heat should approach the thermodynamic limit. However, for large τp the reset operation fails giving a wrong logic output. In these cases, where the error probability is high, the produced heat is clearly below the Landauer limit. Inset shows the obtained relation between error probability (1 − Ps) and produced heat. The data are compatible with the minimum energy required for a given error probability as predicted by Eq. 1, represented by dashed line.
Mentions: In Fig. 3(a) we present the average heat produced for the reset operation as function of the lateral alignment of the counter magnet Δx. When the system is aligned closely to perfection (i.e., Δx ≈ 0) we estimate a heat production slightly above kBT and below two times QL. Asymmetrizing the potential, by means of setting Δx ≠ 0, the heat produced tends to decrease reaching values this time below QL. However, in this conditions the error rate in performing the reset operation have a major role, in fact in this configuration the probability of success, Ps, decrease rapidly. This is represented by the color map of dots in Fig. 3(a), where green represents higher success rate while blue represents a higher probability of error. In Fig. 3(b) the success rate of the reset operation is reported as function of the lateral alignment. Solid violet circles represent the overall success rate while red and black symbols represent the error rate for resetting to 1 or to 0 respectively. Circles are used to report the error probability for the same initial and final state while crosses are used for 0 to 1 and 1 to 0 transitions. For instance let us consider the case where Δx < 0: the counter magnet is moved towards the right and as a consequence the 0 state is more favorable respect the 1 state. From Fig. 3(b) we can see that for Δx < 0 the probability of resetting toward 0 is almost 100% while the probability of resetting toward 1 decreases rapidly reaching values below 50%. The same behavior is present in the case Δx > 0, where the counter magnet is moved to the left, where the state 1 is more favorable.

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