  The quantum Jarzynski equality and the Crooks relation are fundamental laws
connecting equilibrium processes with nonequilibrium fluctuations. They are
promising tools to benchmark quantum devices and measure free energy
differences. While they are well established theoretically and also
experimental realizations for few-body systems already exist, their
experimental validity in the quantum many-body regime has not been observed so
far. Here, we present results for nonequilibrium protocols in systems with up
to sixteen interacting degrees of freedom obtained on trapped ion and
superconducting qubit quantum computers, which test the quantum Jarzynski
equality and the Crooks relation in the many-body regime. To achieve this, we
overcome present-day limitations in the preparation of thermal ensembles and in
the measurement of work distributions on noisy intermediate-scale quantum
devices. We discuss the accuracy to which the Jarzynski equality holds on
different quantum computing platforms subject to platform-specific errors. The
analysis reveals the validity of Jarzynski's equality in a regime with energy
dissipation, compensated for by a fast unitary drive. This provides new
insights for analyzing errors in many-body quantum simulators.
