Abstract
Here, I test Landauer’s 1961 hypothesis that erasing a symmetric one-bit memory requires work of at least \(kT \ln 2\). This experiment uses a colloidal particle in a time-dependent, virtual potential created by a feedback trap to implement Landauer’s erasure operation. In a control experiment, similar manipulations that do not erase can be done without work.
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Notes
- 1.
The asymptotic work W of a “reset” operation with success rate p is \( W = kT [ \ln (2) + p \ln (p) + (1- p )\ln (1-p)]\). See Chap. 8.
- 2.
The free energy change between final and initial states is \(\Delta F=\Delta E- T \, \Delta S\), with the stochastic system entropy \(S = -k\sum _i p_i \ln p_i\). We normalize S by k, making it dimensionless. The sum is over all states in the system (here, two states—particle in left well or in right well). In our case, \(\Delta E = 0\) because we consider cyclic operations, but \(\Delta S = S_\mathrm{final} - S_\mathrm{initial} = 0\) for the no-erasure protocol (since, at the end of the cycle, \(p_0 = p_1 = 0.5\) implies \(S_\mathrm{final} = S_\mathrm{initial} = \ln 2\)) and \(\Delta S = -\ln 2\) for the full-erasure protocol (since, at cycle end, \(p_0 = 0\) and \(p_1 = 1\) implies \(S_\mathrm{final} = 0\)).
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Gavrilov, M. (2017). High-Precision Test of Landauer’s Principle. In: Experiments on the Thermodynamics of Information Processing. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63694-8_4
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