Low-temperature ordering conjecture for weakly coupled mixed-chaotic Hamiltonian systems

Let a Hamiltonian dynamical system exhibit mixed chaos, with chaotic trajectories and islands of regularity in its phase space. Suppose the system is weakly coupled to a thermal bath at sufficiently low temperature. Low-temperature ordering conjecture. The dynamics will settle into islands of order. The paper develops numerical evidence and physical intuition for this claim using five in silico dynamical systems of varied structure and dimension; it presents the claim as a conjecture tested computationally, so its general validity remains open.