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 Λ 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.