P - V criticality of first-order entropy corrected AdS black holes in massive gravity

We consider a massive gravity black hole in four-dimensional anti-de Sitter space and study the effect of thermal fluctuations on the thermodynamics of the black hole. We consider thermal fluctuations as logarithmic correction terms in the entropy. We analyze the effect of logarithmic correction on thermodynamics potentials like Helmholtz and Gibbs which are found decreasing functions. We study critical points and stability and find that the presence of logarithmic correction is necessary to have stable phase and critical point.