A Chaos Energy Bound for Any Classical/quantum Hamiltonian Theory

A bound on energy dependence of chaos

We conjecture a chaos energy bound, an upper bound on the energy dependenceof the lyapunov exponent for any classical/quantum system with finite / large number of degrees of freedom.The conjecture states that the exponent grows no faster than linearly in the total energy in the high energy limit.In other words, the exponent in satisfies.This chaos energy bound stems from thermodynamicconsistency of out-of-time-order correlators (otoc s) and applies to any classical/quantum system with finite / large number of degrees of freedom under plausible physical conditions on the hamiltonians.We provide arguments supporting the conjecture for generic classically chaotic billiards and multi-particle systems.