  We propose a formalism which defines chaos in both quantum and classical
systems in an equivalent manner by means of adiabatic transformations. The
complexity of adiabatic transformations which preserve classical time-averaged
trajectories (quantum eigenstates) in response to Hamiltonian deformations
serves as a measure of chaos. This complexity is quantified by the (properly
regularized) fidelity susceptibility. Our exposition clearly showcases the
common structures underlying quantum and classical chaos and allows us to
distinguish integrable, chaotic but non-thermalizing, and ergodic regimes. We
apply the fidelity susceptibility to a model of two coupled spins and
demonstrate that it successfully predicts the universal onset of chaos, both
for finite spin $S$ and in the classical limit $S\to\infty$. Interestingly, we
find that finite $S$ effects are anomalously large close to integrability.
