A consistent flow of entropy

A common approach to evaluate entropy in quantum systems is to solve a master-Bloch equation to determine density matrix and substitute it in entropy definition. However, this method has been recently understood to lack many energy correlators. The new correlators make entropy evaluation to be different from the substitution method described above. The reason for such complexity lies in the nonlinearity of entropy. In this paper we present a pedagogical approach to evaluate the new correlators and explain their contribution in the analysis. We show that the inherent nonlinearity in entropy makes the second law of thermodynamics to carry new terms associated to the new correlators. Our results show important new remarks on quantum black holes. Our formalism reveals that the notion of degeneracy of states at the event horizon makes an indispensable deviation from black hole entropy in the leading order.