To understand the effect of third order Lovelock gravity, P-V criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case β → ∞ is performed for the sevendimensional black holes. It is shown that, for the spherical topology, P-V criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of P-V criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss-Bonnet black holes. For k = 0, there would be no P-V criticality. Interesting findings occur in the case k = −1, in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the P-v diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of α, the entropy is always positive for any specific volume v. Since no P-V criticality exists for k = −1 in Einstein gravity and Gauss-Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss-Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and "swallow tail" behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research. a

Effects of the dimensionality on the Joule-Thomson expansion are discussed in detail by considering the case of d-dimensional charged AdS black holes. Specifically, we investigate three important aspects characteristic of the Joule-Thomson expansion. Namely, the Joule-Thomson coefficient, the inversion curves and the isenthalpic curves. We utilize two different approaches to derive the explicit expression of the Joule-Thomson coefficient and show that both approaches are consistent with each other. The divergent point and the zero point of the Joule-Thomson coefficient are discussed. The former is shown to reveal the information of Hawking temperature while the latter is depicted through the so-called inversion curves. Fine structures of the inversion curves are disclosed in the cases d > 4. At low pressure, the inversion temperature increases with the dimensionality d while at high pressure it decreases with d. The ratio between minimum inversion temperature Tmin and the critical temperature Tc is discussed with its explicit expression obtained for d > 4. Surprisingly, it is shown that the ratio is not always equal to 1/2 but decreases with the dimensionality d. Moreover, isenthalpic curves of d > 4 are shown to expand toward higher pressure when the dimensionality d increases.