Perturbed thermodynamics of charged black hole solution in Rastall theory

We study the thermodynamics of a charged black hole surrounded by a perfect fluid in Rastall theory and investigate three different cases of quintessence, dust and radiation fields. By considering thermal fluctuations, we study the corrected thermodynamics of the system. We investigate the effects of thermal fluctuations on the black hole stability, phase transition and critical points. We show that the thermal fluctuations increase instability of the black hole and may yield to the second order phase transition. We also compare our result with uncharged cases to find the effects of the black hole charge on the thermodynamics quantities. We find that large black holes behave like a Van der Waals fluid, while for the small black hole where thermal fluctuations become important, there is no Van der Waals behaviour. Finally, we briefly discuss about geometric thermodynamics to obtain corrected scalar curvature.