From 1871 to 1878, Gibbs worked on thermodynamics, introducing geometrical methods, thermodynamic surfaces, and criteria for equilibrium. He developed the concept of Gibbs free energy and other thermodynamic potentials in the analysis of equilibrium. Gibbs also built the foundation of modern vector calculus and studied the electromagnetic theory of light.

After writing several papers, Gibbs changed the focus of his research from thermodynamics to statistical methods. In 1884, he introduced the "Gibbs principle" for statistical entropy, canonical, and microcanonical statistical distributions. In 1898, he studied the "Gibbs phenomenon" in the convergence of Fourier series. By 1902, Gibbs published "Elementary Principles of Statistical Mechanics", from which the foundation of statistical mechanics was built.