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。非平衡统计力学的最新理论进展，结合平行的实验和计算进展，已经将该领域从传统的近平衡系统转移到更广泛的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法律，而热棘轮和相关模型的研究提供了一个微观的理解如何热涨落可以转换为定向运动，而不违反热力学第二定律。这些进展不仅提供了一套新的工具，适用于技术和根本的重要性问题，但也提出了新的研究方向。该研究将强调三个主题相关的系统，驱动远离热平衡的外部参数的随时间变化。特别是，该研究将：开发理论工具，用于分析随机泵中产生的电流;设计和实施一种新的蒙特卡罗方案，用于使用非平衡模拟来生成试验动作的复杂系统的有效采样;以及探索微观系统中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下，随机泵可以用来模拟酶参与跨膜运输，或化学反应网络;和采样复杂系统的数值困难出现在从蛋白质折叠到自旋玻璃旅行推销员问题。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。这些活动包括在美国和国外的机构举办讲座;开展服务活动;建立一个社区驱动的网站，专门介绍自由能源计算方法;开发教育资源。最后，该奖项支持的研究将直接有助于本科生和研究生的培训，他们将提高他们的分析和计算技能，并拓宽他们的统计力学知识，同时解决智力挑战性问题。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。非平衡系统和过程是普遍存在的，涵盖了从材料生长到化学系统的广泛现象，这些化学系统表现出有趣的空间模式，再到维持生命的过程。非平衡态热力学研究具有多个自由度的大型复杂系统随时间变化的问题。这一领域的大多数传统研究都集中在接近平衡态的系统上，即系统几乎是一个稳态系统。相比之下，该奖项支持的研究将为远离热力学平衡的系统开发模型。这项理论研究将应用于软物质物理学的广泛实验应用，包括自然和人工纳米级电机和机器的应用。随着合成轮烷、索烃、分子开关和未来纳米级机器的其他预期组件的能力的增加，需要一个用于此类系统的外部控制的一般理论框架。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。这些活动包括在美国和国外的机构举办讲座;开展服务活动;建立一个社区驱动的网站，专门介绍自由能源计算方法;开发教育资源。最后，该奖项支持的研究将直接有助于本科生和研究生的培训，他们将提高他们的分析和计算技能，并拓宽他们的统计力学知识，同时解决智力挑战性问题。

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.