Dynamical Systems and Statistical Mechanics: an LMS Durham Research Symposium

牛顿的运动定律已经不够好了。今天，统计力学处于物理科学的核心。例如，对给定系统的分子行为的统计分析有助于解释为什么热从热的物体流向冷的物体(热力学)，云是如何随着它们的运动而移动的，等等。其他应用领域包括金融市场的行为或复杂的生物系统。在玻尔兹曼、吉布斯和许多其他人提出统计力学理论100多年后，这一理论的基础仍然是活跃研究的主题。最终的目标是从微观的运动方程中完整地解释热力学和统计力学行为。另一方面，动力系统传统上处理的变量要少得多，并且采取更确定的方法。典型的问题可能如下所示。如果球的速度和方向只以一种特定的已知方式取决于它的位置，那么什么时候会有起点使物体恢复到原来的位置和原来的速度和方向？近年来，动力系统理论有了长足的进步，这与统计力学之间的界限变得模糊了，例如在研究混沌方面。例如，通过研究热流或天气模式，已经建立了进一步的联系。与使用动力系统的简单模型系统所证明的结果类似，最终可能有助于证明统计力学的一些关键假设是正确的。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也被证明是非常成功的。建议举行一次为期10天的会议，重点讨论动力系统和统计力学领域之间的交叉，由C.Beck(Mary Queen)、C.Dettmann(布里斯托尔)和M.Pollicott(Warwick)组织。这将把领先的海外和英国研究人员聚集在一起，进行一段时间的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处的领域。讲座内容整齐，有充分机会进行讨论、合作和非正式讨论。会议成果将以两种方式直接分发。将有一个积极管理和易于访问的网站，其中将包含与会者名单、演讲摘要和其他相关信息。将出版一本书，对所讨论的材料进行描述和扩展，从而为会议提供更持久和更详细的记录。此外，预计受会议主题启发的几篇前沿文章将出现在研究期刊上。预计这次会议将对世界上对我们理解和预测复杂物理系统行为具有根本重要性的领域的研究提供一个重大而持久的推动。

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.