Feedback in Small Systems -A Stochastic Thermodynamic Perspective

Sammanfattning: Recent advances in nanotechnology and the accompanying development oftechniques that operate and manipulate systems on the micro- and nanometer scale have driven the development of stochastic thermodynamics. This isa theory that can describe small systems far from equilibrium, where the fluctuations are of the same order of magnitude as the mean values. Stochasticthermodynamics can be used to prove that it is possible to utilize fluctuationsto extract heat from a reservoir by the application of feedback. In this thesis,two model systems are investigated, namely molecular motors and feedbackapplied 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 definitionof the efficiency of macroscopic motors with the definition of efficiency for information ratchets. This enables to determine the regime in which efficiencyis maximized (power stroke, Brownian rectifier, or a combination of both). Itis found that the efficiency is strongly dependent on the step length of themolecular motor. The greater the distance between steps, the more dominant the fluctuations, and the more important the feedback is in obtaininghigh efficiencies. The results are compared with biological molecular motors(kinesin, myosin II and myosin V) and it is found that these motors work ina regime where efficiency is maximized for a power-stroke-assisted Brownianrectifier mechanism. Furthermore, the way in which this model can be used toemulate a possible experimental realization of Maxwell’s demon using opticaltweezers is described. A model of an artificial bidirectional molecular motoris studied, where the input work is determined by the difference in free energyof different ligand concentrations. It is demonstrated that feedback could increases the efficiency of this motor tremendously, while the thermodynamiccost of information is negligible, as in this case, the difference in free energyis much greater than the entropy cost of feedback, kT ln 2. A driven two state model operated under ideal feedback, i.e., without measurement errorsand with perfect implementation, is also analysed, from a single discrete measurement via consecutive discrete measurements, to the limit of continuousmonitoring. In the latter regime, simple analytical expressions are derived forthe work and power bounds, and it is shown that the reduction in dissipationis maximized in the continuous limit. The analysis is then expanded to themore experimentally relevant case of non-ideal implementation. A fluctuation theorem for discrete feedback in unzipping experiments is experimentallydemonstrated via single-molecular force spectroscopy on short DNA hairpins.Preliminary results for continuous monitoring experiments are presented