The equation of state with non-equilibrium methods

Jarzynski's equality provides an elegant and powerful tool to directly compute differences in free energy in Monte Carlo simulations and it can be readily extended to lattice gauge theories to compute a large set of physically interesting observables. In this talk we present a novel technique to determine the thermodynamics of strongly-interacting matter based on this relation, which allows for a direct and efficient determination of the pressure using out-of-equilibrium Monte Carlo simulations on the lattice. We present results for the equation of state of the $\mathrm{SU}(3)$ Yang-Mills theory in the confined and deconfined phases. Finally, we briefly discuss the generalization of this method for theories with fermions, with particular focus on the equation of state of QCD.