Within the dynamism and bustle of the everyday world being 'far-from-equilibrium' is a common state of affairs. In science non-equilibrium means that some system has been pushed away from a thermodynamically stable state. If this push is gentle, then the response of the system will be a perturbation of its well-understood equilibrium physics. However, if the push is violent then a near-endless zoo of complex effects can arise that are both conceptually and phenomenologically distinct from any behaviour displayed near equilibrium. For this reason, non-equilibrium physics plays a crucial role in many fields ranging from the cosmology of the early universe to glass formation in dense fluids. Yet questions about non-equilibrium phenomena can often appear untameable compared to equilibrium problems due to the lack of a universal organising principle governing them.

In this research area we are particularly interested in non-equilibrium physics exhibited by many-body systems, where the constituent particles behave quantum mechanically and strongly interact with one another. This is a highly challenging domain not least because interactions cause the particles to correlate their ensemble behaviour, so they cluster or avoid each other as well as delocalising. As a consequence, new collective effects can emerge over the entire system responsible for rich behaviour at equilibrium. For electrons in solids high-temperature superconductivity and magnetic ordering can result, while for 'synthetic solids' of ultra-cold atoms trapped in an optical lattice, interactions can induce superfluidity and insulating phases.

Given this, it is justifiably anticipated that an even vaster and largely unexplored landscape of spectacular non-equilibrium effects in many-body systems awaits. Such new physics is becoming increasingly accessible in sophisticated experiments where systems can be strongly and controllably driven, while its subsequent dynamics are measured on short timescales. One approach is to shine intense laser pulses on materials to energetically excite them via periodic modulation. Another way is to sandwich a system between larger thermal reservoirs with widely differing temperatures and chemical potentials that drive strong particle and energy currents through it. Our research aims to develop the theory underpinning what novel and potentially technologically useful properties emerge in these exotic regimes.

A number of important long-term questions guide our studies. What transient spatially inhomogeneous ordered states can emerge in systems driven by ultra-short pulses? What non-equilibrium stationary phases are stabilised by continuous periodic driving and dissipation into a thermal reservoir? How efficient and robust can a quantum system act as a nanoscale autonomous thermal machine operating between two thermal reservoirs? What is the nature of entanglement, correlations and quantum mutual information in these new states as compared to those in equilibrium? And can these properties be exploited to enable accurate classical simulation of these quantum many-body systems so their behaviour can be predicted and optimised? Such new avenues of investigation hold the promise of aiding the delivery of quantum-enhanced microscopic devices for information processing, in-situ power generation and wasted energy recovery.