What does an increase in entropy (S) indicate about a system?

An increase in entropy (S) signifies that a system has become more disordered or randomized. In thermodynamic terms, entropy is a measure of the number of ways a system can be arranged, reflecting the level of uncertainty or randomness associated with the microscopic configurations of the system. As a system undergoes a change that results in increased entropy, it indicates that the molecules within the system are moving more freely, occupying a greater variety of states. For instance, when ice melts into water, there is an increase in the entropy because the ordered structure of solid ice transitions to the more disordered and freely moving molecules of liquid water.

This concept is essential because it aligns with the second law of thermodynamics, which states that in an isolated system, the total entropy will tend to increase over time, leading to more probable (disordered) configurations. Consequently, an increase in entropy means that the system is moving towards a state of greater disorder, making the given choice the correct interpretation of an increase in entropy.