An isolated system is the one in which neither energy nor matter can enter/leave the system.

∆S is the change in entropy. Entropy is a measure of randomness or disorder in a system. More the randomness, more is the entropy of a system.

According to the second law of thermodynamics the total entropy can never decrease over time for an isolated system.

The total entropy is constant in ideal cases where the system is in equilibrium, or undergoing a reversible process and approaches 0 at absolute zero only.

In all spontaneous processes, the total entropy always increases and the process is irreversible.

Therefore, ∆S is always greater than 0, ∆S>0.