Formality and generality of damping-induced order in mixed-chaotic systems

Ascertain the generality and establish rigorous conditions under which adding weak damping leads to emergent order in mixed-chaotic Hamiltonian systems, beyond low-dimensional cases.

Background

Prior mathematical intuition suggests that weak damping can induce order in mixed-chaotic systems, but much of the past work has focused on low-dimensional examples. The authors observe that it is unclear how broadly or formally this intuition applies and aim to place it on firmer physical footing by connecting damping to low temperature via the Einstein relation.

Clarifying the scope and formal underpinnings of this intuition would help determine how widely such damping-induced order can be expected in many-body and more complex settings.