In reality more heat is disappearing down the drain instead of going into work. Since the entropy is a variable of state, each state has its well-defined entropy S A and S B . The first part be the irreversible process that actually takes place and the second part be a reversible change one could make by interfering with the system. Since the whole circular change is irreversible, the ring integral of heat change divided by temperature is less than 0. In the last step we use the fact that the system is isolated, i.e. there is no change of the heat.
Irreversible processes make sure that the entropy actually always increases.
If the universe is an isolated thermodynamic system, then its entropy must increase all the time. Since that is not at all like the universe we know, it follows that the universe is not infinitely old. Statistical mechanics is closely related to thermodynamics. Statistical mechanics looks at the microscopic construction of thermodynamic systems. Since there are a large number of identical microscopic particles, statistical arguments are used.