Probability: The Heart of Chemistry #SoME2

Edwin Jaynes formalized maximum entropy principle as inference method—choosing probability distributions maximizing entropy subject to known constraints. Josiah Willard Gibbs applied entropy maximization deriving statistical mechanics. Information theorists recognize entropy maximization as fundamental inference principle. Physicists employ the principle deriving equilibrium distributions from first principles.

Ludwig Boltzmann derived the probability distribution for energy states in thermal equilibrium in the late 1800s. James Clerk Maxwell developed related velocity distributions for gas molecules. Statistical mechanics pioneers connected microscopic dynamics to macroscopic thermodynamics. Chemists use Boltzmann distributions predicting molecular population distributions across energy levels.

Josiah Willard Gibbs developed partition function formalism connecting statistical mechanics to thermodynamics. Statistical mechanicians use partition functions calculating thermodynamic properties from molecular parameters. Physical chemists compute partition functions predicting chemical equilibria. Computational chemists calculate partition functions from quantum mechanical energy levels.