Which formula represents the statistical definition of entropy according to Boltzmann?

The statistical definition of entropy according to Boltzmann is represented by the formula S = k ln(W), where S is entropy, k is the Boltzmann constant, and W is the number of microscopic configurations (or microstates) that correspond to a thermodynamic system's macroscopic state.

This equation captures the idea that entropy is a measure of the disorder or randomness of a system. As the number of microstates (W) increases, the entropy (S) also increases, indicating greater disorder. The natural logarithm (ln) in the formula reflects how entropy scales with the number of available configurations — it captures the logarithmic nature of relationships in statistical mechanics.

The alternatives that involve temperature or rearrangements do not align with the fundamental statistical mechanics principle set forth by Boltzmann. The key here is focusing on the relationship between microstates and entropy, which is succinctly captured in the chosen formula.