Feedback in Small Systems -A Stochastic Thermodynamic Perspective

Recent advances in nanotechnology and the accompanying development of
techniques that operate and manipulate systems on the micro- and nanometer scale have driven the development of stochastic thermodynamics. This is
a theory that can describe small systems far from equilibrium, where the fluctuations are of the same order of magnitude as the mean values. Stochastic
thermodynamics can be used to prove that it is possible to utilize fluctuations
to extract heat from a reservoir by the application of feedback. In this thesis,
two model systems are investigated, namely molecular motors and feedback
applied to unfolding and refolding of DNA hairpins pulled with optical tweezers in an attempt to ascertain how efficiently can this be done.
A definition of efficiency is introduced, which unites the classic definition
of the efficiency of macroscopic motors with the definition of efficiency for information ratchets. This enables to determine the regime in which efficiency
is maximized (power stroke, Brownian rectifier, or a combination of both). It
is found that the efficiency is strongly dependent on the step length of the
molecular motor. The greater the distance between steps, the more dominant the fluctuations, and the more important the feedback is in obtaining
high efficiencies. The results are compared with biological molecular motors
(kinesin, myosin II and myosin V) and it is found that these motors work in
a regime where efficiency is maximized for a power-stroke-assisted Brownian
rectifier mechanism. Furthermore, the way in which this model can be used to
emulate a possible experimental realization of Maxwell’s demon using optical
tweezers is described. A model of an artificial bidirectional molecular motor
is studied, where the input work is determined by the difference in free energy
of different ligand concentrations. It is demonstrated that feedback could increases the efficiency of this motor tremendously, while the thermodynamic
cost of information is negligible, as in this case, the difference in free energy
is much greater than the entropy cost of feedback, kT ln 2. A driven two state model operated under ideal feedback, i.e., without measurement errors
and with perfect implementation, is also analysed, from a single discrete measurement via consecutive discrete measurements, to the limit of continuous
monitoring. In the latter regime, simple analytical expressions are derived for
the work and power bounds, and it is shown that the reduction in dissipation
is maximized in the continuous limit. The analysis is then expanded to the
more experimentally relevant case of non-ideal implementation. A fluctuation theorem for discrete feedback in unzipping experiments is experimentally
demonstrated via single-molecular force spectroscopy on short DNA hairpins.
Preliminary results for continuous monitoring experiments are presented