The Principle of Increase of Entropy states that for any real, spontaneous (irreversible) process in an isolated system, the total entropy always increases. $\Delta S_{total}>0$

• For an ideal, reversible process, $\Delta S_{total}=0$.
• Entropy never decreases in an isolated system. This gives 'time' a direction, as processes always move towards states of higher entropy (and thus higher probability/disorder).