טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentShahaf Asban
SubjectInteracting Stochastic Pumps
DepartmentDepartment of Physics
Supervisors Professor Podolsky Daniel
Dr. Rahav Saar
Full Thesis textFull thesis text - English Version


Abstract

Recent years have seen great progress in the understanding of small systems away from equilibrium. Modern technology have opened researchers a window into the molecular world where smaller and shorter scales can be probed than ever before. Under the collective name of stochastic thermodynamics, theoretical tools have been developed to capture their behavior mathematically under a simple yet powerful formalism. One of the most influential results of which are the fluctuation theorems. Fluctuation theorems unveil the specific manner in which symmetries are broken, typically time-reversal symmetry. This alliance of theory and experiment offer new approaches that can be used to study fundamental problems related to the out-of equilibrium dynamics of small systems. Our contributions to this important field are discussed below.


The first topic deals with the conditions under which periodically driven interacting systems would result in directed motion. Motivated by a beautiful experiment on artificial molecular motors, a universal condition for dynamical pumping of current of thermally activated systems was derived. In such systems, instantaneous breaking of translational symmetries does not yield directed motion, which is guaranteed by the existence of the no pumping theorem (NPT). The experiment suggested that interactions play a significant role and may alter this condition. In the first direction of research, a many-body version of the model, with local interactions has been considered. Surprisingly, the NPT found for noninteracting systems, has been found to hold also for many particle systems with local interactions. In the case of the hydrodynamic limit of the above systems, we have shown that the particle density follows a nonlinear diffusion equation. Using this equation, one may derive an expression for the current which is subsequently used to derive a hydrodynamic version of the NPT.


The second part of this thesis reviews the symbiotic relations between information theory and statistical physics; studying the possibility of using information gained on the state of a system to improve free energy calculations. Nonequilibrium free energy calculations are known to suffer from poor convergence due to the need to sample rare events. We examine if the inclusion of measurement and feedback can improve the convergence of free energy calculations based on processes away from equilibrium. Surprisingly, we find that discarding realizations with unwanted outcomes can result in improved convergence compared to calculations based on the Jarzynski’s equality. We argue that the observed improved convergence is closely related to Bennett’s acceptance ratio method, which was developed without any reference to measurements or feedback.