Ok, I know this is an old post, but I want to point out that it is *shown* in Avengers that Thanos (or at least the guy working right under him) are definitely torturing Loki to keep him in line (and long distance at that). Look at the scene in the middle of the movie when he talks to the guy that’s like his go-between to Thanos, he seems to be using an illusion or something to talk to them and when they harm him, he responds like he has been harmed by this action.
Thanos is *not* a nice person and wouldn’t hesitate to torture someone if it was easier for him. Loki is powerful, yes, but Thanos is stronger, smarter, and more experienced. The Loki that got caught by Thanos is not the mature Loki who can manipulate the good guys into doing his dirty work for him (I’m referencing the comics and animated shows here), he is a young Loki who is hurt and vulnerable. Loki shows through all of the movies that he’s in, that he’s not really as on top of things as it seems.
Loki’s exhaustion, obvious pain, and determination to go through with Thanos’ plan are likely because he has *no choice*. He’s gotten in over his head with Thanos (who he cannot charm, trick, or bargain with) and he sees no way out.
One of the things that really shows this is the scene where he stabs Thor (though honestly, it’s shown throughout the movie). Loki almost seems like he wants to go with Thor and you see something similar to pain flash across his face when her realizes he *can’t* go with Thor, and mentions that it’s too late.
Through out the movie Loki’s language focuses on that fact that *he* can’t stop this. That this is going to happen and there is nothing *he* or anyone else can do about it. There is also his line “I am *burdened* with glorious purpose.” Remember that Loki is someone who uses his words to get things done, this means that he speaks carefully and deliberately.
Let’s also look at Loki’s behavior thus far. Up until he fell in with Thanos, Loki was always the one calling the shots. Loki manipulated people into conflict, but he rarely actually made any moves by himself (i.e. manipulating Thor into going to face the Frost Giants [Side note: I don’t think he actually planned for Thor to get exiled or for him to cause such a huge problem]). In Avengers we see Loki moving out in the open, which we all *know* is not where he prefers working, but he’s also doing so while obviously ill and exhausted.
To kinda bring this to a close, since I went on much longer than I intended to. Loki got way in over his head with Thanos and was basically doing what he could to survive. Thanos likely did at least harm Loki to keep him in line, if not actually torture him. I *doubt* that Thanos used Loki’s Jotun herritage to get new torture methods, especially because you can still hurt a Jotun just fine without specialized torture methods.
P.S. If anything just suddenly cuts off and doesn’t complete, it’s likely because I had another thought train pop up in the middle of typing. Also, I may have missed some thing because there’s a *lot* to unpack when it comes to Loki in his first two movies.