As a physicist I really started to scratch my head at some point. Good that you realized, gauge theory does not help with economics.

It is actually not a surprise, since gauge theory is applied to Hamilton mechanics (Lagrangians) and thus a part of physics that does not have entropy production. Or does not have a net entropy flow out of the system or into it. These theories are time-symmetric and there is no way to derive an irreversible process from these fundamental dynamics. We don't know if this is the final answer and the universe is like that, whatever new fundamental physics we discover can be build with these assumptions and if true the whole impression of time evolution being clearly directed and the world being unable to come back to previous states is just a result of special initial conditions of our universe. This is the Einstein/Spinoza picture of the world.

In economics this is obviously not true. Energy/Matter/You-Name-It flows out of the system. You can burn stuff, but in the end it becomes carbon dioxide and then you can only revert this process by putting in more energy than previously gained (this is not true for the universe, since the universe does not lose the heat dissipated away from the earth for example, but the boundaries of our economic system are left in that way...).

Arbitrage cycles are a result of a out of equilibrium state and these cycles relax back to equilibrium and this process is irreversible and produces entropy. Often it seems like these cycles never relax but that is only true in these parts of our economy where new information keeps coming in. You can always find a local probe volume (physicist style :D) in which nobody wants to trade, sure the whole economy is never at rest, but the same applies for our physical world.