Probing phase transitions of regular black holes in anti-de Sitter space with Lyapunov exponent

Abstract: We investigate the relationship between thermodynamic phase transitions and the Lyapunov exponent of charged regular anti-de Sitter black holes in quasi-topological gravity. Our results show that the Lyapunov exponent displays oscillatory behavior during phase transitions. Moreover, along the coexistence curve the Lyapunov exponent changes discontinously and continuously at the critical point. Near the critical point, the Lyapunov exponent follows a power-law behavior with a critical exponent of 1/2, suggesting its role as an order parameter and encodes information on black hole phase transitions.