Thermodynamics of Euler-Heisenberg AdS black hole surrounded by quintessence field using shadow

We extend the black hole solution of Euler-Heisenberg gravitational theory in AdS space-time by introducing quintessence field in it and studied thermodynamics and phase structure using both semi classical analysis and shadow formalism by considering Lambda as thermodynamic pressure. We compare the results obtained by these two methods. The N-type change in temperature for P<P-c can be seen. The nature of Gibbs free energy ensures the second order phase transition for P<P-c, which agrees with the temperature behaviour and then derived heat capacity, Joule-Thomson coefficient to study local stability and heating (or cooling) effect. Assuming black hole as a thermodynamic engine, we calculate the efficiency of Carnot cycle and Rankin cycle and study the impact of various black hole parameters on them. We also studied Ruppeiner thermodynamic geometry in {S,Q} thermodynamic phase space to study the BH at molecular level.