Noise and Complexity in Nonequilibrium Systems: Small Systems, Reaction Kinetics

许多现代技术依赖于非平衡系统中的复杂现象。一些最有趣的现象出现在波动起突出作用的小系统中，通常的（平衡）统计力学定律不起作用。本项目关注小型非平衡装置的热力学效率，以及反应-亚扩散问题的介观描述，其中非线性、随机性和远离平衡的复杂性是重要的。涨落定理规定了导致系统变得更有序的涨落概率，如果系统足够小，这种效应是可以观察到的。这个项目将研究涨落定理是否能揭示非平衡状态下小系统的效率，以及有限时间和随机热力学的思想是否可以用来建立新的普遍结果。这些问题将在经典状态下的机械和化学输运中得到解决，最重要的是，在量子状态下的输运性质。经典状态的焦点将包括通过渗出的传输，以及化学驱动的布朗电机和泵的微观描述。在量子体系中，焦点包括粒子通过量子点的输运以及涨落定理与量子测量理论的关系。将寻求包含这两种情况的非线性响应的普遍性。将寻求区分各种亚扩散情景的措施，例如分形介质中的运动与具有淬火无序的规则介质中的运动。一些解析和数值方法将被应用。虽然一些数值方法是标准的，但其他方法将涉及多尺度方法的发展，这些方法可以处理这项工作所需的空间和时间尺度范围。解决本提案中提出的问题将导致对随着新的理论、实验和数值方法的发展而出现爆炸性增长的问题的新见解。这项工作的更广泛影响有两个方面。一个是代表人数不足的群体成员的密切和广泛参与。这项工作的参与者在指导未被充分代表的群体的本科生、研究生和研究生研究方面有着长期的记录，并设计了各种各样的机构倡议来加强这一点。他们坚定地承诺继续这些努力。另一个方向是研究人员与欧洲和拉丁美洲的科学家成功建立的广泛的跨学科合作网络。作为欧洲科学基金会在静力学和动力学方面的一项重大工作的三个召集人之一，其中一名高级调查员发挥了重要作用，以及私家侦探与拉丁美洲科学家的参与，使这一切成为可能。

Many modern technologies rely on complex phenomena in systems out of equilibrium. Some of the most interesting phenomena arise in small systems in which fluctuations play a prominent role and the usual laws of (equilibrium) statistical mechanics do not work. This project focuses on thermodynamic efficiency in small non-equilibrium devices, and on mesoscopic descriptions of reaction-subdiffusion problems,in which nonlinearity, stochasticity, and complexity away from equilibrium are important. The Fluctuation theorem specifies the probability of fluctuations that cause a system to become more ordered, an effect that is observable if a system is sufficiently small. This project will examine whether the Fluctuation theorem can reveal something about the efficiency of small systems in the non-equilibrium regime, and whether the ideas of finite time and stochastic thermodynamics can be used to establish new universal results. These questions will be addressed for mechanical and chemical transport in the classical regime and, most importantly, for transport properties in the quantum regime. The focus in the classical regime will include transport via effusion, and the microscopic description of a chemically driven Brownian motors and pumps. In the quantum regime the foci include transport of particles through quantum dots and the relation of the fluctuation theorem to the theory of quantum measurement. Universality of nonlinear responses that encompass both regimes will be sought. Measures to differentiate among various subdiffusive scenarios such as motion in a fractal medium versus motion in a regular medium with quenched disorder will be sought. A number of analytic and numerical methods will be applied. While some of the numerical methods are standard, others will involve the development of multiscale approaches that can handle the range of spatial and temporal scales required for this work. Solution of the problems posed in this proposal will lead to new insights to questions that have seen an explosive growth of interest with the development of new theoretical, experimental, and numerical methods. The broader impact of this work has two aspects. One is the close and extensive involvement of members of underrepresented groups. The participants in this efort have long track records in mentoring undergraduate, graduate, and postgraduate research of members of underrepresented groups and designing a variety of institutional initiatives to enhance that. They have a strong commitment to continue these efforts. Another direction lies in the extensive collaborative interdisciplinary network that the investigators have successfully established with scientists in Europe and Latin America. This is made possible by the essential role of one of the senior investigators as one of three conveners of a major European Science Foundation effort in statics and dynamics, and the involvement of the P.I. with scientists in Latin America.