Dynamical Systems and Statistical Mechanics: an LMS Durham Research Symposium

动力系统和统计力学：LMS 达勒姆研究研讨会

• 批准号: EP/D040027/1
• 负责人: John Bolton
• 金额: $ 7.27万
• 依托单位: Durham University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD040027%2F1
• 关键词: Dynamical; Systems; Statistical; Mechanics; LMS

Newton's laws of motion are no longer good enough. Today, statistical mechanics lies at the heart of the physical sciences. For instance, a statistical analysis of the behaviour of the molecules of a given system helps explain why heat flows from a hot body to a cold one (thermodynamics), how clouds move as they do, and much more besides. Other areas of application include the behaviour of financial markets or complex biological systems.More than 100 years after the formulation of the theory of statistical mechanics by Boltzmann, Gibbs, and many others, the foundations of this theory are still the subject of active research. The ultimate objective is to completely explain, for instance, thermodynamic and statistical mechanics behaviour from the microscopic equations of motion.Dynamical systems, on the other hand, have traditionally dealt with many fewer variables, and take a more deterministic approach. A typical problem might be the following. If the speed and direction of a ball depends only on its position in a particular known way, when will there be starting points for which the body returns to its original position with its original speed and direction?In recent years there has been considerable progress in the theory of dynamical systems, and the boundary between this and statistical mechanics has become blurred, for instance in the study of chaos. Further links have been established through, for example, the study of heat flow or weather patterns. Results similar to those which have been proved for simple model systems using dynamical systems may ultimately help to justify some of the key assumptions of statistical mechanics. On the other hand, some formal mathematical methods borrowed from the theory of the statistical mechanics of heat flow have turned out to be very successful for the analysis and description of dynamical systems. It is proposed to hold a 10 day conference concentrating on the intersection between the areas of dynamical systems and statistical mechanics, organised by C. Beck (Queen Mary), C. Dettmann (Bristol) and M. Pollicott (Warwick). This will bring together leading overseas and UK researchers for a period of concentrated research activity and interchange of ideas. The programme will be designed to focus on areas which show particular promise, and where interactions between different groups are likely to be of most benefit. There will be an uncluttered lecture programme, with ample opportunities for discussions, collaborations and informal talks.The results of the meeting will be directly distributed in two ways. There will be an actively-managed and easily accessible website, which will contain a list of participants, abstracts of talks and other relevant information. A lasting and more detailed record of the meeting will be provided by the publication of a book describing and expanding on the material discussed. In addition, it is expected that several cutting-edge articles inspired by the subjects covered in the meeting will appear in research journals. The conference is expected to provide a major lasting fillip to world research in areas of fundamental importance for our understanding and ability to predict the behaviour of complex physical systems.

牛顿运动定律不再足够好。今天，统计力学是物理科学的核心。例如，对给定系统的分子行为进行统计分析有助于解释为什么热量从热物体流向冷物体（热力学），云如何移动，等等。其他应用领域包括金融市场行为或复杂的生物系统。在玻尔兹曼、吉布斯和其他许多人提出统计力学理论100多年后，这一理论的基础仍然是积极研究的主题。最终的目标是从微观运动方程中完全解释热力学和统计力学行为。另一方面，动力学系统传统上处理的变量要少得多，并且采用更确定性的方法。一个典型的问题可能如下。如果一个球的速度和方向仅仅以一种特定的已知方式取决于它的位置，那么什么时候会有物体以它的原始速度和方向返回到它的原始位置的起始点呢？近年来，动力系统理论取得了长足的进步，而动力系统理论与统计力学之间的界限已经变得模糊，例如在混沌的研究中。例如，通过研究热流或天气模式，已经建立了进一步的联系。类似于那些已经证明了简单的模型系统使用动力系统的结果可能最终有助于证明统计力学的一些关键假设。另一方面，从热流统计力学理论中借用的一些形式化的数学方法在分析和描述动力系统方面已经证明是非常成功的。建议举行一个为期10天的会议，集中讨论动力系统和统计力学领域之间的交叉点，由C。Beck（Queen玛丽），C. Dettmann（布里斯托）和M.波利科特（沃里克）。这将使领先的海外和英国研究人员聚集在一起，集中研究活动和思想交流。该方案的设计将侧重于显示出特别希望的领域，以及不同群体之间的互动可能最有益的领域。会议将有一个简洁的演讲计划，有充分的讨论、合作和非正式会谈的机会。会议的结果将通过两种方式直接分发。将有一个积极管理和容易进入的网站，其中将载有与会者名单、会谈摘要和其他有关信息。将出版一本书，对讨论的材料进行描述和扩充，以提供会议的持久和更详细的记录。此外，预计研究期刊上将发表几篇受会议所涉主题启发而撰写的前沿文章。预计这次会议将在对我们理解和预测复杂物理系统行为的能力具有根本重要性的领域为世界研究提供一个重大的持久刺激。