Clausius defined entropy as a measure of irreversibility, where it increases in irreversible processes and remains constant in reversible ones like Carnot's engine. Schrödinger's concept of negentropy links life to entropy reduction by consuming energy, but its mathematical basis remains unclear. Boltzmann's entropy formula, \(S = k_B ln W\), quantifies disorder via microstates. Applying this to Dyson's cell model—a Markov chain with three equilibrium states—involves counting configurations. For a system of 8 sites with 4 empty, 2 active, and 2 inactive, entropy is \(S = k_B ln(420) \approx 6.04k_B\).

This bridges thermodynamic principles to discrete systems, offering insights into entropy dynamics in processes like life.