Modeling Thermodynamic Phase Transitions via Lyapunov Exponents in Nonlinear Electrodynamic Black Holes

In the present analysis, we revisit the Lyapunov exponents characterizing the chaos of both massless and massive particles in the background of a nonlinear electrodynamics black hole and investigate their connection to the black hole thermodynamic phase transitions. In addition to the free energy, we analyze the behavior of the Lyapunov exponents for massive and massless particles, which quantify the chaos and instability of their orbits around the black hole. Our analysis shows that, across the phase transition, the Lyapunov exponents become multivalued, with distinct branches corresponding to different black hole phases. We further find that the discontinuity in the Lyapunov exponent serves as an order parameter exhibiting universal behavior, with a critical exponent of (1/2) near the critical point. These results demonstrate that the Lyapunov exponents provide an effective probe of the phase transition.