homework and exercises - Average force and pressure in a 3D box due to quantum non-interacting particles

A gas of non-interacting quantum particles occupies a box with lengths $L_1, L_2, L_3$. Calculate its energy and thus the average force and pressure exerted by the gas on the walls of the box.

I have this as a solved example but the steps aren't explained and I'm confused. I tried looking online for a similar derivation but couldn't find anything. The idea is to express the energy and calculate the force as its gradient but it does so taking the derivatives with respect to the lengths $L_1, L_2, L_3$ which I find puzzling. I mean if we had an expression for a potential at any points in the space in the box than I would understand this approach but as it is, I don't see it!

Here's the expression for energy which is then differentiated w.r.t to the $L$'s to get the force:

$$E = \frac{\hbar ^2}{2m} \left( \left( \frac{n_1}{L_1} \right) ^2 + \left( \frac{n_2}{L_2} \right) ^2 + \left( \frac{n_3}{L_3} \right) ^2 \right)$$