(79g) On Relating Polymer Dynamics to Non-Equilibrium Statistical Mechanics Using the Jarzysnki Equality

The study of complex fluids has benefited tremendously from the machinery of non-equilibrium statistical mechanics and other concepts in traditional physics. In the context of polymer dynamics, analytical tools such as renormalization group theory have been used to accurately predict (for example) the scaling exponent for a self-avoiding walk, while other approaches such as Fokker-Planck formalism have provided a starting point for kinetic theory and Brownian dynamics simulations of chain dynamics. In this work, we apply modern non-equilibrium statistical mechanics to polymer dynamics via the Jarzynski equality, which allows for calculation of free energy changes from non-equilibrium measurements. We utilize the Jarzynski equation to compute the free energy (an equilibrium concept) of a polymer molecule as a function of chain extension during far-from-equilibrium processes, such as chain stretching in strong hydrodynamic flows. To demonstrate the Jarzynski approach, we use Brownian dynamics simulations of discretized bead-spring chains to model dsDNA dynamics. Furthermore, we demonstrate that calculation of polymer free energy as function of chain extension allows for determination of chain force-extension elastic relations. Overall, this work shows that the formalism of non-equilibrium statistical mechanics may be applied to obtain information regarding chain elasticity from transient stretching trajectories of single chains in flow.