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Article overview
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Principle of Minimal Work Fluctuations | | Gaoyang Xiao
; Jiangbin Gong
; | | Date: |
3 Jun 2015 | | Abstract: | Understanding and manipulating work fluctuations in microscale and nanoscale
systems are of both fundamental and practical interest. For example, in
considering the Jarzynski equality $langle e^{-eta W}
angle=e^{-eta
Delta F}$, a change in the fluctuations of $e^{-eta W}$ may impact on how
fast the statistical average of $e^{-eta W}$ converges towards the
theoretical value $e^{-eta Delta F}$, where $W$ is the work, $eta$ is the
inverse temperature, and $Delta F$ is free energy difference between two
equilibrium states. Motivated by our previous study aiming at the suppression
of work fluctuations, here we obtain a principle of minimal work fluctuations.
In brief, adiabatic processes as treated in quantum and classical adiabatic
theorems yield the minimal fluctuations in $e^{-eta W}$. In the quantum
domain, if a system initially prepared at thermal equilibrium is subject to a
work protocol but isolated from a bath during the time evolution, then a
quantum adiabatic process without energy level crossing (or an assisted
adiabatic process reaching the same final states as in a conventional adiabatic
process) yields the minimal fluctuations in $e^{-eta W}$, where $W$ is the
quantum work defined by two energy measurements in the beginning and at the end
of the process. In the classical domain where the classical work protocol is
realizable by an adiabatic process, then the classical adiabatic process also
yields the minimal fluctuations in $e^{-eta W}$. Numerical experiments based
on a Landau-Zener process confirm our theory in the quantum domain, and our
theory in the classical domain explains our previous numerical findings
regarding the suppression of classical work fluctuations [G.~Y.~Xiao and
J.~B.~Gong, Phys. Rev. E {f 90}, 052132 (2014)]. | | Source: | arXiv, 1506.1185 | | Services: | Forum | Review | PDF | Favorites | |
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