Work statistics for the adiabatic assumption in nonequilibrium many-body theory

Keldysh field theory, based on adiabatic assumptions, serves as a widely used framework for addressing nonequilibrium many-body systems. Nonetheless, the validity of such adiabatic assumption when addressing interacting Gibbs states remains a topic of contention. Interestingly, the knowledge of work statistics developed in nonequilibrium thermodynamics helps us to quantitatively explore this problem. Consequently, we deduce a universal theorem delineating the characteristics of evolutions that transition an initial Gibbs state to another. Based on this theorem, we analytically ascertain that adiabatic evolutions fail to transition a noninteracting Gibbs state to its interacting counterpart. However, the adiabatic evolution remains a superior approximation relative to its nonadiabatic counterparts. Numerics verifying our theory and predictions are also provided. Furthermore, our findings render insights into the Gibbs state preparation within the domain of quantum computation.