  The fluctuation theorems, and in particular, the Jarzynski equality, are the
most important pillars of modern non-equilibrium statistical mechanics. We
extend the quantum Jarzynski equality together with the Two-Time Measurement
Formalism to their ultimate range of validity -- to quantum field theories. To
this end, we focus on a time-dependent version of scalar phi-four. We find
closed form expressions for the resulting work distribution function, and we
find that they are proper physical observables of the quantum field theory.
Also, we show explicitly that the Jarzynski equality and Crooks fluctuation
theorems hold at one-loop order independent of the renormalization scale. As a
numerical case study, we compute the work distributions for an infinitely
smooth protocol in the ultra-relativistic regime. In this case, it is found
that work done through processes with pair creation is the dominant
contribution.
