Explain the concept of entropy

Entropy is a fundamental concept in statistical mechanics, representing the measure of disorder or randomness in a system. Explain the concept of entropy, including its statistical definition in terms of microstates and macrostates, and its relationship with thermodynamic properties such as temperature and energy. Discuss the second law of thermodynamics, which states that the entropy of an isolated system always increases over time, and its implications for the arrow of time and the irreversibility of natural processes. Furthermore, explore the role of entropy in understanding phase transitions, such as the melting of solids or the condensation of gases, and its applications in fields ranging from information theory to biology.