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

许多现代技术依赖于系统中不平衡的复杂现象。一些最有趣的现象出现在小系统中，在这些系统中，涨落扮演着突出的角色，(平衡)统计力学的通常定律不起作用。本项目关注小型非平衡装置的热力学效率，以及反应-次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。涨落定理规定了使系统变得更加有序的涨落的概率，如果系统足够小，这种影响是可以观察到的。这个项目将考察涨落定理是否能揭示小系统在非平衡状态下的效率，以及有限时间和随机热力学的思想能否被用来建立新的普遍结果。这些问题将针对经典体系中的机械和化学输运，以及最重要的量子体系中的输运性质进行讨论。经典理论的重点将包括通过渗流的传输，以及对化学驱动的布朗马达和泵的微观描述。在量子区域中，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。将寻求涵盖这两种制度的非线性反应的普遍性。将寻求区分各种亚扩散场景的措施，例如在分形介质中的运动和在具有淬灭无序的规则介质中的运动。将应用一些解析和数值方法。虽然有些数值方法是标准的，但其他方法将涉及开发能够处理这项工作所需的空间和时间尺度范围的多尺度方法。本提案中提出的问题的解决将导致对随着新的理论、实验和数值方法的发展而引起人们爆炸式增长的兴趣的问题的新见解。这项工作的更广泛影响有两个方面。其一是代表人数不足的群体成员的密切和广泛参与。这一efort的参与者在指导本科生、研究生和研究生对代表性不足群体成员的研究并设计各种机构倡议以加强这一点方面有着长期的记录。他们坚定地致力于继续这些努力。另一个方向在于调查人员成功地与欧洲和拉丁美洲的科学家建立了广泛的跨学科协作网络。这是因为其中一名高级调查人员作为欧洲科学基金会(European Science Foundation)在静力学和动力学方面的重大努力的三名召集人之一所发挥的关键作用，以及P.I.与拉丁美洲科学家的参与。

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.