Visual Understanding: Microstates and Entropy

Boltzmann's equation connects the microscopic world of particle arrangements to the macroscopic concept of entropy:

LOW ENTROPY (Ordered) Ω ≈ 1 (few microstates) HIGH ENTROPY (Disordered) Ω >> 1 (many microstates) Time S increases Phase Space Volume Small volume Low entropy Large volume High entropy S = kB ln Ω

The number of ways to arrange particles increases dramatically as they become disordered. Entropy (S) measures this increase logarithmically.