Ford, IJ;
Minor, DS;
Binnie, SJ;
(2012)
Symmetries of cyclic work distributions for an isolated harmonic oscillator.
European Journal of Physics
, 33
(6)
pp. 1789-1801.
10.1088/0143-0807/33/6/1789.
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Abstract
We have calculated the distribution of work W done on a 1D harmonic oscillator that is initially in canonical equilibrium at temperature T, then thermally isolated and driven by an arbitrary time-dependent cyclic spring constant κ(t), and demonstrated that it satisfies P(W) = exp (βW)P( − W), where β = 1/kBT, in both classical and quantum dynamics. This differs from the celebrated Crooks relation of nonequilibrium thermodynamics, since the latter relates distributions for forward and backward protocols of driving. We show that it is a special case of a symmetry that holds for non-cyclic work processes on the isolated oscillator, and that consideration of time reversal invariance shows it to be consistent with the Crooks relation. We have verified that the symmetry holds in both classical and quantum treatments of the dynamics, but that inherent uncertainty in the latter case leads to greater fluctuations in work performed for a given process.
| Type: | Article |
|---|---|
| Title: | Symmetries of cyclic work distributions for an isolated harmonic oscillator |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/0143-0807/33/6/1789 |
| Publisher version: | http://dx.doi.org/10.1088/0143-0807/33/6/1789 |
| Language: | English |
| Additional information: | Copyright 2012 IOP Publishing Ltd |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1379243 |
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