  Due to technological needs, nanoscale heat management, energy conversion and
quantum thermodynamics have become key areas of research, putting heat pumps
and nanomotors center stage. The treatment of these particular systems often
requires the use of adiabatic expansions in terms of the frequency of the
external driving or the velocity of some classical degree of freedom. However,
due to the difficulty of getting the expressions, most works have only explored
first-order terms. Despite this, adiabatic expansions have allowed the study of
intriguing phenomena such as adiabatic quantum pumps and motors, or electronic
friction. Here, we use nonequilibrium Green's functions, within a
Schwinger-Keldysh approach, to develop second-order expressions for the energy,
heat, and charge currents. We illustrate, through two simple models, how the
obtained formulas produce physically consistent results, and allow for the
thermodynamic study of unexplored phenomena, such as second-order
monoparametric pumping.
