If that isn't a correct interpretation of your argument, then the rest of this won't make a lot of sense.
The reason this sort of thermodynamics arguments fails for me is that the economy isn't really the amount of cash flowing through it, rather cash is a proxy for GDP not the economy itself. GDP is a function of productivity and effort. In simpler terms we can have our fictional worker 'Bob' who is anxious and fearful so he scrapes along with a minimum wage job that he hates, versus 'Alt-Bob' who is engaged and excited about his career and is building a future retirement nest egg. With the same 'worker population' of '1' we get two very different GDPs.
One theory is that UBI will make the anxious Bob less anxious and fearful and able to make better choices about their future. If you look at some of the work on how people who are anxious about the amount of money they have a hard time making good choices I refer you to the book 'Scarcity: Why having so little means so much.' it is a good read in general because it applies to anything, even 'free time' as a resource.