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We calculate the maximal Lyapunov exponent for a bulk system of 256Lennard-Jones particles in constant energy molecular dynamics simulations deepinto the supercritical state. We find that the maximal Lyapunov exponentundergoes a crossover, and that this crossover coincides with the dynamicalcrossover at the Frenkel line from liquid physics. We explain this crossover interms of two different contributions to dynamical instability: diffusion in theliquid-like state below the Frenkel line, and collisions in the gas-like stateabove. These results provide insight into the phase space dynamics far from themelting line and densities where rare-gas approximation are inapplicable.

Crossover of dynamical instability and chaos in the supercritical state