Force autocorrelation function in linear response theory and the origin of friction

TL;DR

This paper explains the physical origin of friction in finite systems using linear response theory, showing that finite mass effects cause the vanishing of the Green-Kubo friction coefficient, and clarifies conditions for finite friction.

Contribution

It reveals that finite mass of the environment causes the vanishing of the Green-Kubo friction coefficient, providing a physical interpretation and conditions for finite friction in linear response theory.

Findings

Finite mass of the environment leads to vanishing Green-Kubo friction coefficient.

Two infinite masses in the liquid suffice for finite friction.

Different friction coefficients for two infinite-mass particles are physically interpreted.

Abstract

Vanishing of the equilibrium Green-Kubo fluctuation expression for the friction coefficient of a massive particle moving in a finite-volume liquid is usually interpreted as an unphysical consequence of the finite volume. Here I show that it is a physical consequence of the finite mass of the rest of the system, which allows it to be dragged by the moving particle. As a consequence, it is sufficient to have two infinite masses in the liquid for the friction coefficient to be finite. In addition, I give the physical interpretation of different friction coefficients for two infinite-mass particles moving in the liquid.