How fast does time flow? Dynamical behaviour in glasses, nano-science and self-assembly

The flow of time is an essential feature of the human experience, and it also lies at the centre of modern physics. Einstein's relativity is concerned with the nature of time as it affects stars and planets, while quantum physics explains that the flow of time in a system may be strongly affected by the actions of an external observer. However, these theories often seem irrelevant for the most striking human experiences of time: we find that living creatures grow old and die, and man-made structures crumble over time. The physical basis of these processes lies in the increase of disorder, or entropy: maintaining ordered structures requires external work, and in the absence of such work, disorder increases inexorably.In the 20th century, deep and elegant theories were built, to quantify entropy, and to understand why we observe an arrow of time pointing from the past to future. However, many important questions remain unanswered. In particular, theories predict which processes will happen in a system, but they do not predict how fast they happen, nor how natural processes might be resisted by humans or machines. My research is concerned with such questions, but most scientists agree that we are still very far from finding full answers to them. For this reason, I consider specific systems in which such questions are relevant. I then aim to combine the results from different systems in order to arrive at general principles.To take one specific example, glass is a material that has fascinated architects, designers, and artists over centuries. On heating, it softens and can flow as a liquid; if it is then rapidly cooled, it hardens into solid glass, retaining the transparency of the liquid, and the flowing shapes that are familiar from vases and ornaments. In this sense, glass lives on the borderline between liquids and solids. For my research, the key point is that liquids obey the arrow of time by flowing downhill, but solids have a fixed shape, and do not flow. If the glass is indeed a liquid, how does it resist flow? If it is a solid, why does it resemble so closely the liquid? These simple-sounding questions are in fact at the core of long-running scientific debates. In particular, it is not known whether there can exist an ideal glass : a liquid that resists time by flowing only infinitely slowly. If it is indeed possible for spontaneous flow to stop completely, this would have fundamental consequences for theories of the arrow of time.For a second example, consider what happens when viruses spread through a population. Inside the cells of infected organisms, molecules assemble spontaneously into ordered structures that are less than a thousandth of a millimetre in size. In turn, these ordered structures will develop into new viruses, allowing infection of other cells or other organisms. Here, time is of the essence: if the virus develops quickly enough then it can kill the cell, while if it develops too slowly, the cell can detect and destroy the virus. These questions may sound essentially biological, but physics has much to contribute here. My research investigates how fast the ordered structures can assemble, and how they might be speeded up or slowed down. The laws of physics seem to set speed limits on assembly, which I aim to exploit and control. Finally, I also consider how insights from biological assembly processes might be applied in man-made structures that are as tiny as biological viruses, with similarly complex structure and functionality. Such structures are difficult to build, but they have been proposed for the next generation of efficient solar cells, or even as building blocks for tiny machines that might be used to fight diseases like cancer. By working towards a theory for the assembly and control of such structures, my research aims both to develop fundamental theories in physics, and to give practical insights in biology and nanotechnology.

Statistical mechanics is a field that brings together ideas from mathematics, physics, chemistry and biology. For example, established theoretical and computational methods can be used to explain the equilibrium properties of materials such as the metals and semiconductors used in microelectronics; colloidal suspensions such as toothpaste and mayonnaise; and biological cell membranes (the flexible outer walls of animal cells, made of fatty molecules). The elegant mathematical structure of the underlying theory places equilibrium statistical mechanics among the great intellectual achievements of the 20th century, while its applications illustrate its central role in support of current work in science and engineering. However, these theories take almost no account of the flow of time: of how fast systems change, and how such changes can be controlled. These questions lie in the realm of non-equilibrium statistical mechanics, and they are the subject of this proposal. The research is exploratory and fundamental, seeking general principles to inform future materials and device design. The impact of these studies in industry and biotechnology will be pursued primarily through contacts with other academics who are closer to the relevant developing technologies. At the same time, my fundamental research builds towards a coherent theoretical picture of the flow of time in physical systems, which would represent a foundation for long-term technological and scientific progress. Thus, while there are many potential routes for realising the impact of this research, each route should be regarded as somewhat speculative. For example, I am currently studying how self-assembly processes can be optimised and controlled. Nano-scale biomolecules known as chaperonins spontaneously self assemble into ordered sheets and filaments. This process is a subject of ongoing studies at NASA's Ames research laboratory, with a view to exploiting these self-assembled structures in future applications of nanotechnology. However, this assembly process is beyond the scope of simple physical theories, so that there are few principles to guide the experimental studies, and progress often requires laborious trial and error. I seek general theoretical insights to guide future experiments in this area. Similarly, my current studies of the glass transition may be applied in the search for the next generation of non-volatile computer memory, built on so-called phase change materials, such as chalcogenides. Such memory stores data by distinguishing between tiny patches of either crystalline or amorphous (glassy) material. However, the stability of these crystal and glass states cannot be deduced a priori and must again be investigated by trial and error. Here too, new theoretical insights would be very helpful in guiding future materials research. As well as these technological implications, I emphasise two indirect impacts of this research. Firstly, the mathematical and logically rigorous skills required in statistical mechanics are extremely valuable outside an academic context. Examples include methods for assessing the likelihood of rare events (with potential relevance to epidemic spreading); quantitative measurements of predictability based on incomplete information, (as required for estimates of financial volatility); and the degree of reproducibility in self-assembled products. The postdoc and PhD students supported by this grant will also develop such skills, enhancing their potential to contribute both to future academic research and to non-academic employment. Finally, I believe that the still-emerging fields of nanotechnology, biophysics and self-assembly have great potential to catch the public imagination, especially as nano-science enters the technological mainstream. The PI is eager to communicate his ongoing work in this area to a wider audience.