# Dynamical Systems and Statistical Mechanics: an LMS Durham Research Symposium

Lead Research Organisation:
Durham University

Department Name: Mathematical Sciences

### Abstract

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.

## People |
## ORCID iD |

John Bolton (Principal Investigator) |