# How to measure force in a Monte Carlo scheme?

Assume the following, simple, 1D system: a particle on a spring, next to a wall, in a heat bath. Now, let's say that we implement a Monte Carlo scheme (Metropolis or other) for the position of the particle. The wall is hard, so whenever there is an attempt to pass it, the attempt will be rejected. My question is, is there a way to compute the average force exerted on the wall by the particle? My guess is that the force is related to the frequency of hitting the wall (in MC timestep units) but can't precisely see how.

One could do this by summing the impulse delivered at each collision. Suppose the particle goes into the collision with velocity $$v$$ (maybe this can be calculated by looking at how far the particle travels in this step). If the wall is inelastic, then the impulse delivered is $$mv$$. If the wall is elastic, then the impulse delivered is $$2mv$$.
• Maybe you could just use the average value of $v$ then. Commented Sep 4, 2020 at 21:35