CAREER: Thermodynamic Limits to Nonequilibrium Response

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

NONTECHNICAL SUMMARY One of the most basic ways scientists learn about a material is to manipulate it and then quantitatively measure how it responds: for example, we say a rubber ball is elastic because it rebounds quickly after we squeeze it, or we say honey is viscous because it flows slowly when we pour it. These materials are examples of systems at equilibrium; left on their own, they are static, passive, and lifeless. For these systems, we have a well-established and robust theoretical framework for analyzing how they respond to external perturbations. However, when we look at the world around us, we see situations that are dynamic, evolving, and alive; these systems are out of equilibrium. Here, our understanding is not nearly as robust, and no comprehensive theory exists. This CAREER award supports theoretical research and education focused on the early steps in developing a novel theoretical framework for understanding response in nonequilibrium systems. The aim of this project is to develop quantitative predictions that capture the trade-offs between how a system responds and how far a system is away from equilibrium. Such quantitative trade-offs not only inform us about fundamental principles of nature, but they also provide guidance on how to design the most responsive nonequilibrium materials. Coupled with experimental data, this approach offers constraints on possible theoretical models. To accomplish this goal, the project will analyze specific theoretical models drawn from diverse disciplines using modern tools of nonequilibrium physics that can then be generalized to make fundamental and generic statements. These activities will involve students, providing cross-disciplinary training in statistical physics and biophysics, as well as mentorship and professional development skills. A major part of this project is a partnership with the University of Michigan Museum of Natural History to create outreach programs that engage the public with the scientific principles that underpin this research. Included is the development of a hands-on museum exhibit as well as an inquiry-based middle school curriculum. TECHNICAL SUMMARY Many of the basic characteristics of any physical system are captured by how the system responds to perturbations. Near thermodynamic equilibrium, response is completely characterized by the nature of spontaneous fluctuations according to the fluctuation-dissipation theorem. This deep connection between response and fluctuations is not only the cornerstone of statistical mechanics and hydrodynamics, but finds practical application in microrheology, spectroscopy and dynamic light scattering. Whereas the fluctuation-dissipation theorem is limited to static near-equilibrium situations, most of the natural world is driven out of equilibrium by the constant consumption of energy. This CAREER award supports fundamental theoretical research and education aimed at unraveling how energy dissipation shapes the response properties of far-from-equilibrium matter. The remarkable utility of the fluctuation-dissipation theorem has led to significant interest in expanding its validity and developing generalizations for nonequilibrium situations. Though to date many of those predictions have been quite formal. This project puts forward a new perspective on how to analyze nonequilibrium matter, allowing the PI to develop informative quantitative bounds on response in terms of the thermodynamic forces driving the system out of equilibrium. In particular, the project focuses on current response and violations of Onsager reciprocity for discrete and continuous dynamics. Systems of interest include nonequilibrium response of diffusing colloidal particles, chemical reaction networks, and processive molecular motors, all of which have important applications across engineering, chemistry, and biology. This work is carried out by combining numerical exploration of model systems with detailed theoretical analysis to make universal thermodynamic statements. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.