  Molecular motors are known to have the high efficiency of energy
transformation in the presence of thermal fluctuation.
  Motivated by the surprising fact, recent studies of thermal ratchet models
are showing how and when work should be extracted from non-equilibrium
fluctuations.
  One of the important finding was brought by Magnasco where he studied the
temperature dependence on the fluctuation-induced current in a ratchet
(multistable) system and showed that the current can generically be maximized
in a finite temperature.
  The interesting finding has been interpreted that thermal fluctuation is not
harmful for the fluctuation-induced work and even facilitates its efficiency.
We show, however, this interpretation turns out to be incorrect as soon as we
go into the realm of the energetics
[Sekimoto,J.Phys.Soc.Jpn.66,1234-1237(1997)]: the efficiency of energy
transformation is not maximized at finite temperature, even in the same system
that Magnasco considered. The maximum efficiency is realized in the absence of
thermal fluctuation. The result presents an open problem whether thermal
fluctuation could facilitate the efficiency of energetic transformation from
force-fluctuation into work.
