Scrambling in nearly thermalized states at large central charge

We study 2d conformal field theory (CFT) at large central charge c and finite temperature T with heavy operators inserted at spatial infinity. The heavy operators produce a nearly thermalized steady state at an effective temperature T ₄₅₅ T. Under some assumptions, we find an effective Schwarzian-like description of these states and, when they exist, their gravity duals. We use this description to compute the Lyapunov exponents for light operators to be 2πT ₄₅₅, so that scrambling is suppressed by the heavy insertions.