The relation between the entropy exchange of an open atmospheric system in non-equilibrium conditions with its environment and the organization of the system is examined in terms of the theory of dissipative structures. In this paper, the integrative form of the entropy balance equation in a form suitable for describing the entropy budget of an atmospheric system as a whole is derived starting from the Gibbs relation, and, as examples, the entropy flows of a West Pacific typhoon and a Bay of Bengal cyclone are calculated. The results show that negative entropy flows have an important effect on the organization of atmospheric dissipative structures and that the evolution of negative entropy flows is a good indicator of the life cycle of an atmospheric system.