Final Activity Report Summary - PHYSCOM (Physics of Communications) The research in this project was centred on the application of methods and tools from statistical physics to the theory of telecommunications. In particular, the complexity that appears in modern wireless and optical communications systems has deep analogies to problems that appeared in trying to understand the physics of disordered metals and heavy nuclei. These tools have very recently started making their way to being applied with great success to understanding how information is transmitted through a cluttered medium, such as an office building or a city, with the use of multiple antennas. In this project, these tools were used to try to understand various aspects of this problem. In one line of work, we analysed the information capacity of a system with multiple transmit and multiple receive antennas when the information travels through random cluttered environments through several paths with different relative delays. We also analysed and got analytic formulas for the statistics of this capacity when the random medium fluctuates in-between. In another line of work, we analysed the various options the transmitter has when he has knowledge of the channel matrix. One option is to 'invert' the matrix, so that the receiver sees no interference from other sources. In this work, we found ways to minimise the total energy transmitted. In a yet other approach, we tried to analyse the behaviour of the transmission when the statistics of the channel varies, from e.g. Gaussian to other types of behaviour. Perhaps our most significant result came from analysing the effects that non-linearities in optical fibre transmission play in information transmission. Although optical fibre networks are at the core of modern communications systems - such as digital telephony and the internet, we do not yet have a clear understanding of the capacity of optical fibres for transmitting information. The noise that inevitably enters in long range transmission through an optical channel fundamentally limits the rate at which information can be sent through the channel without error. Current technologies operate at transmission rates much lower than this natural upper bound, but constant technological progress will allow us to operate at higher rates in the future. The objective of our research is to get a better understanding of the highest possible rate of long range information transmission in optical fibres, by using a combination of methods from statistical physics, information theory, and nonlinear differential equations. We have been able to get an estimate of this rate significantly higher compared to the ones previously obtained in the context of currently used wavelength division multiplexing (WDM) systems under otherwise similar assumptions, and we continue to refine our model in ways that bring it closer to real-life systems. Our work and the work of our colleagues in this field should help reveal the true potential of the hundreds of millions of kilometres of optical fibre that make modern communications possible.