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By using the scattering of a scalar field, we discuss the thermodynamics andovercharging problem in a 4D Gauss-Bonnet AdS black hole in both the normalphase space and extended phase space. In the normal phase space, where thecosmological constant and Gauss-Bonnet parameter are fixed, the first law andthe second law of thermodynamics are valid. In addiction, the black hole cannotbe overcharged and the weak cosmic censorship conjecture is valid. In theextended phase space, where the cosmological constant and Gauss-Bonnetparameter are treated as the thermodynamic variables, the first law is stillvalid. However, the second law is indefinite. Moreover, after the scattering ofthe scalar field, the extremal black hole cannot be overcharged and thenear-extremal black hole can be overcharged.

Thermodynamics with pressure and volume of 4D Gauss-Bonnet AdS Black Holes under the scalar field