You say that "Net current equal to zero" is good property of the themodynamic equilibrium.
Let our system be an empty container (no gravitation) in thermal equlibrium with termostat at finite temperature t0. Let us put in the container a rotating rigid sphere.
The net current of the matter is zero, but the system is not in equilibrium. There are local macroscopic currents of matter. After a long time, due to exchange of the radiation between rigid sphere and the termostat, the sphare will lost their rotation. This is a classical example of a system with net currents equal to zero and in non equilibrium state, because local macroscopic currents of matter are nonzero.
The magnetic domain is a system in equilibrium state, with net current equal to zero and with macroscopic local currents nonzero.
So it seems to me that in some system of quantum origin macroscopic currents may be nonzero (e.g. total current as you want is zero, but local macroscopic currents are nonzero) in state of thermal equilibrium.
do yop see the difficulties? we have to distigiuish between quantum and cllassical systems to chatracterize thermal equlibrium.
In physics, we call "thermodynamics" something else. We call it "statistical mechanics." Meaning macroscopic and predictable based on statistics. Before you read further, please just consider this notion: "equilibrium" is *defined* in thermodynamics as a state where there is no net flow. Trying to prove that there is a net flow is just trying to prove non-equilibrium. There's no reason to try and say that there are counterexamples. That's like trying to say that a dog is really a cat. The very word "equilibrium" means that all the flows are equal in all parts of the system, in and out. If you find a counterexample that exists, then by definition the system is NOT IN EQUILIBRIUM. So if you find a counterexample, then you've found a system that is not in thermal equlibrium. Done.
Now, for the rest of this.
You will get macroscopic currents greater than zero, but you just don't seem to grasp the concept of NET currents being zero. If there were a nonzero net current, you'd have charge building up somewhere or (in the case of heat currents, spontaneous heat buildup). That would cause a massive voltage buildup spontaneously, which never happens.
Then, you posed a problem that makes no sense, because any matter falling into your sphere would transform its energy into thermal energy. Current of matter and rotational motion = change in thermal energy = not in equilibrium...and yet all the laws of physics are satisfied. In order to slow the rotating object you propose, you would need friction and translation of the energy of the matter to the sphere into thermal energy. The sphere would necessarily heat up. The problem doesn't even relate remotely because you didn't consider what transfer of mass would do to the bodies being transferred to and from. Stop thinking in one dimension all the time about this.
Your third paragraph (single sentence) indicates that you also missed out on the whole thing about how a macroscopic NET current would not be nonzero in a magnetic domain or there would be a severe charge buildup and ridiculous fluctuation in electromagnetic fields. Please don't embarrass yourself with that line of questioning.
There are no difficulties here. The things you propose are insane. There's no system in which the total current in a steady state (steady state = equilibrium) where the "local macroscopic" (as you call it) is nonzero and the macroscopic is zero. You haven't proposed anything new or groundbreaking at all. I don't have to invoke the minds who have been thinking on these problems for hundreds of years to tell you that your examples are just plain wrong on the face of it, and I'm getting tired of discussing it. I mean, maybe you're angling for a chapter in the book I'm writing on science crackpots...these questions definitely fall under that category, but you'd probably not be using this forum if you had an actual degree and at least had studied the topic to the Bachelor's degree level. I hate to slam a questioner, but after about several rounds of the same question I have to tell you to not bother sending another "challenge" (and I use the word loosely) to the zeroth law of thermodynamics my way. It's...pathetic.