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He worked on statistical mechanics and vector analysis. His work on vector analysis, using ideas of Grassmann, produced a system much more easily applied to physics than that of Hamilton. His work on statistical mechanics was important in providing a mathematical framework for quantum theory and for Maxwell's theories.
Gibbs' most important papers were Graphical Methods in the Thermodynamics of Fluids (1873), A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces (1873) and On the Equilibrium of Heterogeneous Substances (1876).
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