This award supports a theoretical research and education program in the field of nonequilibrium statistical mechanics with a focus on soft condensed matter. Recent theoretical advances in nonequilibrium statistical mechanics, combined with parallel experimental and computational progress, have shifted the field from its traditional focus on near-equilibrium systems to a wider consideration of systems far from thermal equilibrium. Fluctuation theorems and nonequilibrium work relations have revealed that such systems satisfy strong and unexpected laws, while the study of thermal ratchets and related models provide a microscopic understanding of how thermal fluctuations can be converted into directed motion without violating the second law of thermodynamics. These advances not only provide a new set of tools to apply to problems of both technological and fundamental importance, but also suggest new directions of research. The research will emphasize three topics related to systems that are driven away from thermal equilibrium by the time-dependent variation of external parameters. In particular, the research will: develop theoretical tools for analyzing currents generated in stochastic pumps; design and implement a novel Monte Carlo scheme for the efficient sampling of complex systems using nonequilibrium simulations to generate trial moves; and, explore basic issues of irreversibility and dissipation in microscopic systems. By investigating and extending these results, the PI will further elucidate the meaning and the role of the second law of thermodynamics, in the context of microscopic systems away from thermal equilibrium.
Because of the very general mathematical formulation of the issues the PI plans to investigate, this research will have impact across a broad range of scientific disciplines. For example, apart from the context of artificial molecular machinery, stochastic pumps can be used to model enzymes involved in transmembrane transport, or chemical reaction networks; and the numerical difficulties of sampling complex systems arise in problems ranging from protein folding to spin glasses to the Traveling Salesman Problem. The PI will continue to engage in activities that promote the progress of science, particularly thermodynamics and statistical mechanics. These include lecture courses at institutions both in the United States and abroad; service activities; launching a community-driven web site devoted to methods for free energy calculations; and developing educational resources. Finally, the research supported under this award will directly contribute to the training of undergraduate and graduate students, who will sharpen their analytical and computational skills, and broaden their knowledge of statistical mechanics, while tackling intellectually challenging problems.
NONTECHNICAL SUMMARY This award supports a theoretical research and education program in the field of nonequilibrium statistical mechanics with a focus on soft condensed matter. Nonequilibrium systems and processes are ubiquitous and encompass a wide range of phenomena from materials growth to chemical systems that exhibit interesting spatial patterns to the processes that sustain life. The research area of nonequilibrium thermodynamics studies time-dependent change of large, complex systems with many degrees of freedom. Most traditional research in this field has focused on systems near equilibrium where the system is almost a steady-state system. In contrast, the research supported under this award will develop models for systems far from thermodynamic equilibrium. This theoretical research will have application to a broad range of experimental applications in soft-matter physics, including applications to natural and artificial nanoscale motors and machines. With increasing capability for synthesizing rotaxanes, catenanes, molecular switches, and other prospective components of future nanoscale machines, there is a need for a general theoretical framework for the external control of such systems. The PI will continue to engage in activities that promote the progress of science, particularly thermodynamics and statistical mechanics. These include lecture courses at institutions both in the United States and abroad; service activities; launching a community-driven web site devoted to methods for free energy calculations; and developing educational resources. Finally, the research supported under this award will directly contribute to the training of undergraduate and graduate students, who will sharpen their analytical and computational skills, and broaden their knowledge of statistical mechanics, while tackling intellectually challenging problems.
Historically, the field of statistical mechanics has focused largely on systems in thermal equilibrium. In recent years, however, increased attention has been given to systems away from thermal equilibrium, and in particular to systems far from thermal equilibrium. The goal of this project was to contribute to the theoretical foundations of nonequilibrium statistical mechanics, with a focus on the nonequilibrium behavior of small systems. We have investigated stochastic pumps, a mathematical framework for describing how artificial molecular machines such as rotaxanes, catenanes and other synthetic molecules with moving parts, can be controlled via the manipulation of temperature, laser light and other macroscopic means. Such machines operate in an environment dominated by random thermal fluctuations, or "noise". We have determined conditions under which these machines can be induced to undergo directed motion. We have also studied the relationship between thermodynamics and information processing, involving questions that trace back to the Maxwell demon paradox in which a hypothetical creature brings about an apparent violation of the second law of thermodynamics by observing the random motions of individual atoms and molecules. We have introduced three different models that elucidate how physical systems might, in principle, act like Maxwell's demon, without actually violating the second law. Finally, we have studied fundamental issues related to both classical and quantum mechanical fluctuation relations. In particular, we have shown that such relations -- which describe the behavior of a system that is driven away from equilibrium -- can be understood very naturally in terms of the rare fluctuations of a system in equilibrium. This research has contributed to a broad understanding of the behavior of systems away from thermal equilibrium. It has also contributed to the education and development of the students and postdoctoral research associated who have been involved in the project.
