Generalized detailed balance relation for black hole horizon's fluctuations

In classical thermodynamics, irreversible processes are accomplished with an increase of entropy and a release of heat into the environment. In the case of black hole thermodynamics, instead, the increase of entropy is related with the absorption of energy from the outside of the black hole. Based on this analogy, the black hole is considered as a thermodynamic open system in the non-equilibrium regime during the absorption. Applying a novel result, we obtain a detailed balance relation for the macroscopic absorption of an astronomical object by an static spherically symmetric black hole. Because of the special characteristic of the thermodynamic system, it is necessary to include an additional term for the entropy produced by the absorption, allowing us to set a lower bound for the entropy production due to internal processes associated to the fluctuation.