Calculation of a fluctuating entropic force by phase space sampling

TL;DR

This paper introduces phase space sampling methods to analyze the fluctuating force distribution exerted by a pinned polymer, revealing its asymmetry and the distinction between mean and most probable forces, thus advancing understanding of entropic forces.

Contribution

The authors develop two novel phase space sampling techniques that accurately capture the equilibrium force distribution of a constrained polymer system, providing new insights into entropic force mechanisms.

Findings

Force distribution is highly asymmetric with tensile and compressive forces.

The mean entropic force differs from the most probable force.

The methods enable unbiased phase space sampling of constrained systems.

Abstract

A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.