Abstract

The collective behaviour of birds, traffic flows, high-temperature superconductivity, heat conduction and perturbations in certain space-times are examples of systems that can be described by quasi-hydrodynamics. Hydrodynamics describes the flow of quantities such as energy, momentum and particle number between regions in local thermodynamic equilibrium; quasi-hydrodynamics studies systems in which some of these quantities may decay or ‘relax’.

In ‘Beyond Hydrodynamics’ (Quasihydro ID: 101030915), inspired by gauge-gravity dualities, I developed a general formalism for quasi-hydrodynamics, focusing on fluctuations around global thermodynamic equilibrium. I incorporated relaxation into steady states, derived certain types of relaxation from kinetic theory, and investigated how constraints such as time-reversal symmetry affect linearised observables. I then extended the research to active matter and gauge-gravity systems in electrically driven steady states.

A complete, non-linear quasi-hydrodynamic theory can describe flows around many driven steady states, in which relaxation is balanced by external forces. However, it remains unclear how thermodynamic concepts apply to such states.

“Further beyond hydrodynamics” (FurtherQuasi) will extend this research to non-linear flows around driven steady states. I will determine the constraints and conditions for stationarity, link the microscopic non-conservation of energy and momentum to macroscopic relaxation, and identify new non-linear flows and instabilities. 
I will combine gauge-gravity duality, numerical simulations and kinetic theory. The project will yield new knowledge, techniques, reusable code and experimental protocols, with applications in active and condensed matter, fluid dynamics, high-energy physics, traffic control and astrophysics.