  The local two-dimensional Poincar\'e algebra near the horizon of an eternal
AdS black hole, or in proximity to any bifurcate Killing horizon, is generated
by the Killing flow and outward null translations on the horizon. In
holography, this local Poincar\'e algebra is reflected as a pair of unitary
flows in the boundary Hilbert space whose generators under modular flow grow
and decay exponentially with a maximal Lyapunov exponent. This is a universal
feature of many geometric vacua of quantum gravity. To explain this
universality, we show that a two-dimensional Poincar\'e algebra emerges in any
quantum system that has von Neumann subalgebras associated with half-infinite
modular time intervals (modular future and past subalgebras) in a limit
analogous to the near-horizon limit. In ergodic theory, quantum dynamical
systems with future or past algebras are called quantum K-systems. The
surprising statement is that modular K-systems are always maximally chaotic.
  Interacting quantum systems in the thermodynamic limit and large $N$ theories
above the Hawking-Page phase transition are examples of physical theories with
future/past subalgebras. We prove that the existence of (modular) future/past
von Neumann subalgebras also implies a second law of (modular) thermodynamics
and the exponential decay of (modular) correlators. We generalize our results
from the modular flow to any dynamical flow with a positive generator and
interpret the positivity condition as quantum detailed balance.
