The second law of thermodynamics says that the entropy of an isolated system never decreases. It either increases until the system reaches thermal equilibrium or, if the system is already in equilibrium, remains constant. We had not yet defined entropy when we gave our initial statement of the second law. We’ve now defined the entropy S in terms of the multiplicity of microstates, and we’ve seen that a system’s evolution toward equilibrium occurs because atomic-level interactions move the system from less-probable (lower multiplicity) to more-probable (higher multiplicity) macrostates. With this in mind, a more precise statement of the second law is
where the equality holds only for a system in thermal equilibrium.