In thermodynamics, Gibbs entropy refers to the statistical formulation of entropy for an ideal gas system of particles as found in American engineer Willard Gibbs 1902 book Elementary Principles in Statistical Mechanics. [1]

1. Gibbs, J. Willard (1901). Elementary Principles in Statistical Mechanics - Developed with Special Reference to the Rational Foundation of Thermodynamics. New York: Dover.

Further reading
‚óŹ Li, Ming, Vitanyi, P.M.B. (1997). An Introduction to Kolmogorov Complexity and its Application (section: 8.4.3: Gibbs Entropy, pgs. 564-65). Springer.

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