  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 find
general bounds on the maximum work and the efficiency of thermodynamic
processes involving black holes that can be derived exclusively from the
knowledge of thermodynamic relations at equilibrium. Since these new bounds
consider the finite duration of the processes, they are more realistic and
stringent than their reversible counterparts. To illustrate our arguments, we
consider in detail the thermodynamic optimization of a Penrose process, i.e.
the problem of finding the least dissipative process extracting all the angular
momentum from a Kerr black hole in finite time. 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.
