In researching this question, I've come across plenty of sources that regurgitate intro econ textbooks that say markets equilibrate to Pareto efficiency in conditions of perfect competition (where specific and minimal definitions are also hard to find). I'm sure they're correct that this happens in perfect competition, but I've also read that various economists have simplified and minimized the conditions necessary for a market to theoretically reach pareto efficiency, but I can't find any details on those.

So what are the least restrictive conditions necessary for all markets that fit those conditions to theoretically progress toward a Pareto efficient equilibrium?