A single backwards-playing movie of a financial crash, an epidemic wave, or a solar cell in action would look completely different from the forward version—and that irreversibility is the core puzzle this Centre for Doctoral Training aims to solve. Most of our scientific understanding of materials, weather, and biology rests on equilibrium assumptions, where systems are stable and reversible. But the real world is full of non-equilibrium systems: cells that age, electronic devices that overheat, financial networks that cascade into collapse. These systems are poorly understood, and existing methods often fail to predict their extreme events. This Centre will train at least 10 PhD students per year to bridge disciplines—mathematics, physics, biology, environmental science—and develop new theoretical, computational, and data-driven approaches to analyse non-equilibrium behaviour. If successful, this training will produce a generation of researchers who can transfer methods between fields, improving predictions of epidemics, extreme weather, drug delivery, and energy conversion. It will also strengthen the UK’s position in an area where countries like the U.S. are already investing heavily. While much of the work is fundamental science, deeper understanding of non-equilibrium systems could eventually underpin more reliable infrastructure, safer financial networks, and better medical diagnostics.
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How do we understand whether epidemics will spread, or predict the likelihood of extreme meteorological events? How do we optimize nano-particles to make them efficient vehicles for targeted delivery of drugs in medical applications? Can we predict how a cell in a specific state will evolve in time, for example whether it will stay healthy or become diseased? How do we prevent over-heating in fast electronic devices, or understand how energy conversion in the next-generation of solar cells might work? Can insights into extreme events in the sciences be used to detect whether a network of financial institutions is close to a crash? These research challenges all relate to non-equilibrium systems. Such systems are typically irreversible, so that if a movie of the system was played backwards it would look very different. For equilibrium systems, on the other hand, a backwards movie would appear much like the original. This lack of an "arrow of time" makes equilibrium systems relatively easy to understand, and indeed most existing methods for predicting e.g. the behaviour of materials are based on the assumption of equilibrium. For non-equilibrium systems, on the other hand, we know much less. They can "age" towards an equilibrium state that is never reached, or exhibit extreme events. The latter are often the result of cascades of collective failure, as illustrated in phenomena ranging from stock market crashes to environmental disasters. As the examples in the first paragraph show, understanding, predicting and controlling non-equilibrium behaviour is an important challenge in many problems across the physical, mathematical, biological and environmental sciences. The starting point for the proposed interdisciplinary Centre for Doctoral Training is, therefore, that significant progress will require researchers that can exploit and strengthen such links between disciplines. They will need to be trained in how to analyse non-equilibrium systems theoretically, via mathematical models, how to study their behaviour via computer simulations, and how to extract information about them from possibly noisy or incomplete data. They will also need to be aware of the important non-equilibrium problems in different disciplines, to see connections, transfer methods and concepts from one application area to another, and develop new approaches. The Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES) will provide the training that such a new generation of researchers will need. In a substantial cohort of at least 10 PhD students per year it will make sure that ideas are exchanged systematically; research projects will be designed to build bridges between different disciplines employing similar methods, or to explore the connections between different approaches that are used to study non-equilibrium systems in the same area. Students will acquire transferable communication and presentation skills, and take part in outreach activities to increase the public understanding of non-equilibrium science. In `open questions sandpits', industry engagement events and dedicated careers events they will also obtain a solid understanding of the priorities of industrial partners working on non-equilibrium systems, and of attractive career paths outside of university. Overall, CANES researchers will emerge with a wide variety of skills that are highly sought after in academia and industry. CANES will also put UK research in non-equilibrium systems on the international map, helping the UK to compete against other countries like the U.S.A. where there is already a significant drive to strengthen research in this area.
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