Gibbs

Gibbs commonly refers to Josiah Willard Gibbs (1839–1903), an American scientist whose work laid foundational ideas in chemical thermodynamics, statistical mechanics, and vector calculus. Gibbs introduced a range of concepts and mathematical formalisms that remain central in physics and chemistry, and he helped establish mathematical rigor in the physical sciences. As a result, several important terms in thermodynamics and mathematics bear his name, and the surname is associated with these ideas in scholarly and educational contexts.

Gibbs free energy, G, is a thermodynamic potential that measures the maximum useful work obtainable from a closed system at constant temperature and pressure. It is used to determine reaction spontaneity and phase stability. The Gibbs phase rule, F = C − P + 2, relates the degrees of freedom of a system to the number of components and phases in equilibrium, and the Gibbs–Duhem equation connects changes in chemical potentials in mixtures.

Gibbs phenomenon refers to the persistent overshoot that occurs when approximating a discontinuous function with a finite Fourier series, particularly near jump discontinuities. It is a well-known effect in harmonic analysis and signal processing, named after Gibbs for early analyses of Fourier series.

Gibbs sampling is a Markov chain Monte Carlo algorithm used to generate samples from high-dimensional probability distributions by iteratively sampling each variable from its conditional distribution. Though named for the Gibbs distribution, the method is a general technique in Bayesian inference and statistical computing.

Beyond these, Gibbs appears as a surname for various other individuals and institutions, and the term is used across fields in reference to the above concepts.