Does Tension Apply in One-Dimensional Particle Systems?

[ehrenfest]

Homework Statement

My stat mech book does a problem where it calculate this quantity F for a system of particles restricted to move in one dimensions using the equation $F = \frac{\partial A}{\partial L}$ where A is the helmholtz free energy. What I am confused about is that I thought F represented tensions, and does tension make sense when you have just a collection of particles moving in 1D i.e. I thought tensions only made sense in the context of strings?

Homework Equations

The Attempt at a Solution

 

[Edward G]

The first law of thermodynamics states that

U = dQ + dW (depending on how you define it)

The dW can be replaced with fdL as a unit of work and when the Helmholtz free energy is differentiated with respect to L at a constant temperature, you get the result for the tension.

The system of particles interact with each other, and moving them from the equilibrium position requires a force, as they will try and return to the equilibrium and this is the tension.