Analogous supercritical crossovers in black holes and water

We investigate the supercritical crossovers for black hole thermodynamics in the supercritical regime beyond the critical point, where small and large black holes are indistinguishable from the conventional viewpoint. We establish a refined supercritical phase diagram that comprehensively characterizes small, large, and indistinguishable black hole phases, whose boundaries are defined by two supercritical crossover lines. The universal scaling laws of the two crossover lines are fully verified using black hole thermodynamics in both the standard consideration and the extended thermodynamic phase space by treating the cosmological constant as a thermodynamic pressure. Remarkable analogies are observed when the supercritical phase diagrams of the two frameworks of black holes are compared to those corresponding to liquid-gas and liquid-liquid phase transitions. The present study can be extended to a variety of more complicated black hole backgrounds and provide valuable insights into the fundamental nature of black hole thermodynamics.