Statistical Mechanics of Systems Far from Equilibrium

远离平衡系统的统计力学

• 批准号: 0414122
• 负责人: Beate Schmittmann
• 金额: $ 55.5万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0414122&HistoricalAwards=false
• 关键词: Statistical; Mechanics; Systems; Far; Equilibrium

This award supports theoretical research on the statistical mechanics of systems far from equilibrium. The unifying theme is the characterization and understanding of complex behavior in interacting many-particle systems driven far from thermal equilibrium. The key challenge is to devise a reliable theoretical framework which predicts macroscopic observables from the microscopic dynamics of statistical systems. Currently, such a link exists only for equilibrium systems, in the form of the extremely successful Gibbs ensemble theory. Finding a similar methodology for the non-equilibrium counterparts is of fundamental significance. Given the ubiquity of non-equilibrium phenomena in the biological, physical, and engineering sciences, progress in this endeavor will have broad, interdisciplinary impact.The research has a dual approach, focusing on simple models on one hand, and application-driven studies on the other. In equilibrium statistical mechanics, minimal models such as the Ising model have played a central role. Thanks to the availability of exact solutions and the principle of universality, they have provided deep insight into phase transitions as well as reliable predictions for many physical systems. To serve as a successful proving ground for real non-equilibrium systems, a good minimal model must capture their essential ingredient, namely nontrivial energy fluxes. Lattice gases with one or several species of particles, whose dynamics is biased by an external drive, achieve this goal: The drive injects energy into the system and the thermal bath absorbs it, so that a non-equilibrium steady state is established. Unlike its equilibrium counterpart, this state breaks a key symmetry: detailed balance. As a consequence, much richer phenomena emerge, offering profound challenges. Examples include unexpected ordered structures, novel non-equilibrium transitions, and surprising behaviors in low dimensions. These will be explored here.As the understanding of these proto-systems improves, more complex features will be added, in order to model physical systems more faithfully. Here, two applications with an interdisciplinary aspect are proposed: Protein synthesis and gas diffusion through aged polymer membranes. Both projects encompass the modeling of actual data, from biochemistry and chemical engineering, expressed through a carefully designed non-equilibrium dynamics. They extend the confines of minimal models by including two characteristics which are critical in many real systems: disorder and open boundaries. The final part of the project aims at the very core of non-equilibrium statistical physics. Using an elegant graph-theoretical representation of arbitrary non-equilibrium steady states, the PI's are addressing a critical fundamental issue, namely, the topology of probability currents in configuration space. While seemingly abstract, this analysis is also geared towards a very practical goal: how to design much more efficient codes for simulating desired non-equilibrium steady states.Three aspects of the project promise to have broader impact. First, any progress in developing a basic theoretical framework for non-equilibrium processes will reverberate far beyond the borders of condensed matter theory. Second, the applied projects address important problems in their respective fields. Finally, the project offers many opportunities for student participation at all levels.%%%This theoretical award addresses fundamental issues in non-equilibrium statistical physics. While equilibrium statistical physics is on a relatively firm foundation, the same cannot be said of non-equilibrium systems. Yet equilibrium systems are all around us, including life itself. In addition to fundamental issues, the research will also address a number of specific applications. Finally, the principal investigators have an exemplary record of working with undergraduate and graduate students, as well as postdoctoral associates. ***

该奖项支持对远离平衡的系统的统计力学的理论研究。统一的主题是描述和理解远离热平衡的相互作用的多粒子系统中的复杂行为。关键的挑战是设计一个可靠的理论框架，从统计系统的微观动力学预测宏观可观测性。目前，这种联系只存在于平衡系统，其形式是极其成功的吉布斯系综理论。为非平衡对应物找到类似的方法具有根本意义。鉴于非平衡现象在生物、物理和工程科学中无处不在，这一努力的进展将产生广泛的跨学科影响。研究有双重方法，一方面关注简单的模型，另一方面关注应用驱动的研究。在平衡统计力学中，像伊辛模型这样的最小模型发挥了核心作用。由于精确解的可用性和普适性原则，它们为许多物理系统提供了对相变的深刻洞察和可靠的预测。为了成功地作为真实非平衡系统的试验场，一个好的最小模型必须捕捉到它们的基本成分，即非平凡的能量通量。含有一种或几种粒子的晶格气体，其动力学受到外部驱动的影响，实现了这一目标：驱动向系统注入能量，热浴吸收能量，从而建立了非平衡稳定状态。与其对应的均衡状态不同，这种状态打破了一个关键的对称性：细节平衡。因此，出现了更丰富的现象，带来了深刻的挑战。例子包括意想不到的有序结构，新奇的非平衡转变，以及低维中令人惊讶的行为。随着对这些原始系统的理解的提高，将添加更复杂的特征，以便更真实地对物理系统进行建模。在这里，提出了两个跨学科的应用：蛋白质合成和通过老化的聚合物膜的气体扩散。这两个项目都包括对来自生物化学和化学工程的实际数据进行建模，这些数据通过精心设计的非平衡动力学来表达。它们扩展了最小模型的范围，包括了在许多真实系统中至关重要的两个特征：无序性和开放边界。该项目的最后部分针对的是非平衡统计物理的核心。PI使用了任意非平衡稳态的一种优雅的图论表示，正在解决一个关键的基本问题，即组态空间中概率流的拓扑。虽然看似抽象，但这种分析也是针对一个非常实际的目标：如何设计更有效的代码来模拟所需的非平衡稳态。该项目的三个方面有望产生更广泛的影响。首先，在发展非平衡过程的基本理论框架方面的任何进展都将远远超出凝聚态理论的范畴。第二，应用项目解决了各自领域的重要问题。最后，该项目为学生提供了许多参与各个层次的机会。%这个理论奖致力于非平衡统计物理的基本问题。虽然平衡统计物理学有相对坚实的基础，但对于非平衡系统就不是这样了。然而，平衡系统在我们周围无处不在，包括生命本身。除了基本问题外，这项研究还将涉及一些具体的应用。最后，首席调查人员在与本科生和研究生以及博士后助理一起工作方面有着堪称典范的记录。***