Theoretical Studies in Far-From-Equilibrium Statistical Mechanics

该奖项支持非平衡统计力学领域的理论研究和教育计划，重点是软凝聚态物质。非平衡统计力学的最新理论进展，结合并行实验和计算的进展，使该领域从传统的关注近平衡系统转向更广泛地考虑远离热平衡的系统。涨落定理和非平衡功关系揭示了这样的系统满足强大的和意想不到的定律，而热棘轮和相关模型的研究提供了一个微观的理解，热波动如何在不违反热力学第二定律的情况下转化为有向运动。这些进步不仅为解决技术和基础问题提供了一套新的工具，而且还提出了新的研究方向。该研究将强调与系统相关的三个主题，这些系统是由外部参数的随时间变化而远离热平衡的。具体而言，研究将：开发分析随机泵中产生的电流的理论工具；设计并实现了一种新的蒙特卡罗方案，用于使用非平衡模拟来生成尝试移动的复杂系统的有效采样；并探讨微观系统的不可逆性和耗散的基本问题。通过研究和扩展这些结果，PI将进一步阐明热力学第二定律在远离热平衡的微观系统中的意义和作用。由于PI计划调查的问题具有非常普遍的数学公式，因此这项研究将对广泛的科学学科产生影响。例如，除了人工分子机械的背景，随机泵可以用来模拟参与跨膜运输或化学反应网络的酶；从蛋白质折叠到旋转玻璃再到旅行推销员问题，对复杂系统进行采样的数值困难都会出现。PI将继续从事促进科学进步的活动，特别是热力学和统计力学。这些课程包括在美国和国外机构的讲座课程；服务活动;推出一个社区驱动的网站，专门介绍自由能计算方法；发展教育资源。最后，该奖项支持的研究将直接有助于培养本科生和研究生，他们将提高他们的分析和计算技能，拓宽他们的统计力学知识，同时解决智力挑战问题。该奖项支持非平衡统计力学领域的理论研究和教育计划，重点是软凝聚态物质。非平衡系统和过程无处不在，涵盖了从材料生长到化学系统的广泛现象，这些系统表现出有趣的空间模式，再到维持生命的过程。非平衡态热力学的研究领域是研究具有多自由度的大型复杂系统的随时间变化。该领域的大多数传统研究都集中在接近平衡的系统上，其中系统几乎是一个稳态系统。相比之下，该奖项支持的研究将开发远离热力学平衡的系统模型。这一理论研究将广泛应用于软物质物理学的实验应用，包括自然和人工纳米级电机和机器的应用。随着合成轮烷、链烷、分子开关和其他未来纳米级机器的潜在组件的能力不断提高，需要一个通用的理论框架来控制这些系统。PI将继续从事促进科学进步的活动，特别是热力学和统计力学。这些课程包括在美国和国外机构的讲座课程；服务活动;推出一个社区驱动的网站，专门介绍自由能计算方法；发展教育资源。最后，该奖项支持的研究将直接有助于培养本科生和研究生，他们将提高他们的分析和计算技能，拓宽他们的统计力学知识，同时解决智力挑战问题。

TECHNICAL SUMMARYThis 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.