Langevin analogy between particle trajectories and polymer configurations

A diffusive trajectory drawn by the generalized Langevin equation (GLE) for a colloidal particle evokes a random fractal of a static polymer configuration. This article proposes a static GLE-like description that enables the generation of a single configuration of a polymer chain with the noise formulated to satisfy the static fluctuation-response relation (FRR) along a one-dimensional chain structure but not along a temporal coordinate. A remarkable point is qualitative differences and similarities in the FRR formulation between the static and the dynamic GLEs. Guided by the static FRR, we further make analogous arguments in light of stochastic energetics and the steady-state fluctuation theorem.

Figure 1

Schematic profiles for a Rouse polymer in tension $T_n$, applied force $f_n$, and local stretching rate $\langle d{x}_n/dn\rangle$: (a) local tension induced by a local external dipole force and (b) uniform tension applied by pulling both the chain ends. The upper figures show profiles for tension or applied force, drawn with a solid black or red broken line, respectively. The corresponding local stretching rate $\langle d{x}_n/dn\rangle$ is displayed in the lower figures. The vertical scales for $T_n$ and $f_n$ are not the same.

Figure 2

Schematic profiles for an SA polymer. Axes and legends are the same as those in Fig. 1.