Boltzmann's Entropy Formula

Boltzmann's entropy formula, \( S = k \ln W \), links a system's entropy (disorder) to the number of microscopic arrangements \( W \) that produce the same overall state. Here, \( S \) measures how disordered or unpredictable a system is, \( k \) is a constant (Boltzmann's constant), and \( \ln W \) indicates the natural logarithm of the possible arrangements. Essentially, the more ways particles can be arranged without changing the system's appearance, the higher the entropy. This formula helps explain why systems tend toward states with more arrangements—higher disorder increases entropy.