A large deviation framework for interacting systems far from equilibrium

It has remained a mystery for the past few decades whether there is a non-equilibrium extension to equilibrium statistical mechanics. Recently, there has been advancements through dynamical relationships between currents and energy dissipation and correspondingly their distributions which comes from a framework called large deviation theory. Within this framework, large deviation functions operate in a similar fashion to the free energy in equilibrium which generates the cumulants for the energy. However, advancements of this theory have been mainly for non-interacting models that are exactly solvable. During my graduate career,I have made advancements towards predicting the fluctuations of interacting systems away from equilibrium. Towards this end, I developed a so-called weighted many body expansion which when combined with an approximate closure allowed for mean-field predictions for the distributions of entropy production and mass current in active matter. The same theory also allowed me to quantify density fluctuations and identify the type of phase transition that occurs in interacting active matter and in a model of 2 dimensional membrane-bound protein condensation. Akin to equilibrium distributions, by quantifying how the large deviation functions scale with system size gives information about the interface. I feel confident that my body of work has progressed the field and has provided a new perspective on a decades old problem