Low-temperature bath induces order in mixed-chaotic Hamiltonian dynamics

Prove that Hamiltonian systems exhibiting mixed chaos, when weakly coupled to a thermal bath at sufficiently low temperature, converge to islands of regularity in phase space and thereby exhibit emergent dynamical order.

Background

The paper bridges thermodynamic and dynamical-systems perspectives by noting that damping and temperature are linked via the Einstein relation, so adding weak damping corresponds to coupling a Hamiltonian system to a thermal bath. In mixed-chaotic systems, islands of regularity coexist with chaotic regions; weak damping breaks Liouville’s theorem and can turn these regular islands into attractors.

The authors provide numerical evidence across five systems (including a many-body example) supporting the conjecture that low-temperature bath coupling selects regular trajectories. They explicitly leave formal proofs of this conjecture to future work, framing it as a central open problem.