Autonomous coarse-grained cooling of the coldest reservoir not restricted by the second law of thermodynamics

Nonequilibrium quantum thermodynamics is an intensively developing field with many applications. We study the dynamics of temperatures and chemical potentials of fermionic reservoirs coupled to an open quantum system on a coarse-grained timescale. We show that systematic heat transfer from the cold reservoir to the hot one is allowed in the problem of heat conductance and results in autonomous temporal cooling of the cold reservoir. We show that during the establishment of thermal and chemical equilibrium, nonmonotone evolution of reservoirs' temperatures and chemical potentials is possible, including changes in reservoirs' temperatures and chemical potentials orderliness. Achieved results can be used in the design of quantum thermal machines and nanoelectronic devices.