Systematic theory of coupled bond-angle and orientational fluctuations

Develop a systematic theory of the coupled bond-angle and orientational stochastic dynamics of unconstrained monopolar autophoretic colloidal N-mers, including the emergent global rotational zero mode and the resulting long-time orientational diffusion and entropy production.

Background

The fixed-geometry reduction gives independent one-dimensional gradient dynamics for the orientational modes and predicts bounded mean-squared fluctuations with vanishing orientational-sector entropy production. In unconstrained simulations, however, bond-angle fluctuations couple positional and orientational degrees of freedom, causing long-time growth of the orientational mean-squared displacement and a nonzero orientational-sector entropy production.

The paper interprets the long-time growth as free rotational diffusion of the entire chain superposed on bounded local angular fluctuations relative to the fluctuating body axis, but does not establish this mechanism analytically. A systematic treatment would clarify the coupled stochastic dynamics beyond the parametric fixed-geometry approximation.