Thermodynamic optimization of a Penrose process: An engineers' approach to black hole thermodynamics

In this work we present a new view on the thermodynamics of black holes introducing effects of irreversibility by employing thermodynamic optimization and finite-time thermodynamics. These questions are of importance both in physics and in engineering, combining standard thermodynamics with optimal control theory in order to find optimal protocols and bounds for realistic processes without assuming anything about the microphysics involved. We work out the details of the thermodynamic optimization of a Penrose process, i.e. the problem of finding the maximum work that can be extracted from a Kerr black hole in finite time. This problem has already been addressed in the case of an isolated black hole. Here we consider the case of a black hole immersed in a reservoir and show that the presence of the reservoir can dramatically improve the work output. We discuss the relevance of our results for real astrophysical phenomena, for the comparison with laboratory black holes analogues and for other theoretical aspects of black hole thermodynamics.