Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

New fluctuation theorems on Maxwell’s demon

With increasing interest in the control of systems at the nano- and mesoscopic scales, studies have been focused on the limit of the energy dissipation in an open system by refining the concept of the Maxwell’s demon. To uncover the underlying physical principle behind a system controlled by a demon, we prove a previously unexplored set of fluctuation theorems. These fluctuation theorems imply that there exists an intrinsic nonequilibrium state of the system, led by the nonnegative demon-induced dissipative information. A consequence of this analysis is that the bounds of both work and heat are tighter than the limits predicted by the Sagawa-Ueda theorem. We also suggest a possible experimental test of these work and heat bounds.