  We study time evolution of distance between thermal states excited by local
operators, with different external couplings. We find that growth of the
distance implies growth of commutators of operators, signifying the local
excitations are scrambled. We confirm this growth of distance by holographic
computation, by evaluating volume of codimension 1 extremal volume surface. We
find that the distance increases exponentially as $e^{\frac{2\pi t}{\beta}}$.
Our result implies that, in chaotic system, trajectories of excited thermal
states exhibit high sensitivity to perturbation to the Hamiltonian, and the
distance between them will be significant at the scrambling time. We also
confirm the decay of two point function of holographic Wilson loops on
thermofield double state.
