Extended phase space of black holes in Lovelock gravity with nonlinear electrodynamics

In this paper, we consider Lovelock gravity in the presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering the cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume, and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot P-v, T -v, and G-T diagrams to study the phase transitions of these thermodynamical systems. We show that the power of the nonlinearity and gravity have opposite effects. We also show how consideration of the cosmological constant, nonlinearity, and Lovelock parameters as thermodynamical variables will modify the Smarr formula and the first law of thermodynamics. In addition, we study the behavior of the universal ratio of P(c)v(c)/T-c for different values of the nonlinearity power of electrodynamics as well as the Lovelock coefficients.