Can we define potentials for non-conservative force?

I got the answer to this. This is rather confusing at first, but is pretty simple. For one dimensional optomechanical systems, the radiation pressure force can be written as- $$textbf F(x)=f(x) hat i$$ which obviously has a zero curl, and hence is conservative for those cases. But the work done by such forces in a cycle can still be non zero, because of the finite cavity decay rate $kappa$.

If we are moving infinitely slowly, the number of photons in the cavity get enough time to follow the functional form $f(x)$ given above and be conservative, but for fast processes, photons take a finite amount of time to catch up with the functional form above, and hence based on how that catching up is related to the system, can result in positive or negative work. And this is the basic principle of optomechanical cooling and heating. $$oint F dx < 0$$ implies cooling and $$oint F dx>0 $$ implies heating.