Abstract
The entropy function for an equilibrium system has a Gibbs-Shannon form; however, there is a long, sometimes contentious debate as to whether the Gibbs-Shannon form applies to systems out of equilibrium. Here, I show my first attempt to directly measure the entropy function form for a system out of equilibrium. In a feedback trap, I confine a silica bead immersed in water in a virtual double-well potential that models a two-state system capable of storing one bit of information. By measuring the average work to erase a controlled fraction of the information, I opened the possibility to isolate directly the change in entropy in a nonequilibrium system and compare it with the Gibbs-Shannon form.
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Notes
- 1.
A similar functional form (probability versus tilt) can be obtained from the trapping potential (Eq. 8.4) as \(p(A, t_{\text {er}}) = p_0 \int _{0}^{\infty }\exp \left[ -U(x,t_\mathrm{er}, A)\right] dx\), where \(t_{\text {er}}\) is the moment when the ergodicity breaks for given cycle time \(\tau \).
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Gavrilov, M. (2017). Partial Memory Erasure: Testing Shannon’s Entropy Function . In: Experiments on the Thermodynamics of Information Processing. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63694-8_8
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DOI: https://doi.org/10.1007/978-3-319-63694-8_8
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